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V°L  XXXI  PSYCHOLOGICAL  REVIEW  PUBLICATIONS 

No.  o  1922 


Psychological  Monographs 

EDITED  BY 

JAMES  ROWLAND  ANGELL,  Yale  University. 

HOWARD  C.  WARREN,  Princeton  University  ( Review ) 

JOHN  B.  WATSON,  New  York  (/.  of  Exp.  Psych.) 

SHEPHERD  I.  FRANZ,  Govt.  Hosp.  for  Insane  ( Bulletin )  and 
MADISON  BENTLEY,  University  of  Illinois  {Index) 


STUDIES  FROM  THE  PSYCHOLOGICAL  LABORA¬ 
TORY  OF  THE  UNIVERSITY  OF  CHICAGO 


The  Conditions  of  Retention 


B!^ 

C.  W.  LUH 

Professor  of  Psychology,  Southeastern  University,  Nanking,  China 


PSYCHOLOGICAL  REVIEW  COMPANY 

PRINCETON,  N.  J. 


Agents:  G.  E.  STECHERT  &  CO.,  London  (2  Star  Yard,  Carey  St.,  W.  C.) 

Paris  ( lo  rue  de  Cond6) 


ACKNOWLEDGMENT 


To  Prof.  H.  A.  Carr  I  wish  to  express  my  deepest  sense  of 
obligation  for  constant  supervision  and  encouragement.  Thanks 
are  also  due  to  my  friends  and  fellow-students  whose  patient 
service  made  this  study  possible.  Dean  J.  R.  Angell  and  Dr.  J. 
R.  Kantor  took  great  interest  in  my  work.  To  them  I  owe  much 
that  cannot  be  conventionally  acknowledged. 


\ 


CONTENTS 


PAGE 

I.  Introduction.  . .  .  • .  i 

II.  The  Amount  of  Retention  as  a  Function  of  the 

Method  of  Measurement .  12 

III.  Retention  as  a  Function  of  the  Degree  of  Learning.  43 

IV.  The  Effect  of  Extending  the  Time  Limit  for  Recall 

upon  the  Amount  of  Material  Recalled .  55 

V.  The  Relation  between  the  Amount  of  Error  and 

Other  Factors .  62 

VI.  The  Duration  and  the  Speed  of  Recall .  68 

VII.  Individual  Differences  and  Correlations .  73 

VIII.  Conclusion .  85 


I.  INTRODUCTION 


The  problem  of  the  present  study  is  to  investigate  the  nature 
of  the  curve  of  retention  under  certain  variable  conditions.  The 
conditions  that  can  be  independently  varied  are  numerous.  Only 
two  series  of  experiments  have  been  systematically  carried  out: 

(1)  Varying  the  methods  of  measuring  the  amount  of  reten¬ 
tion  and 

(2)  Varying  the  degree  of  mastery  in  the  original  learning. 

As  established  by  Ebbinghaus,1  the  curve  of  retention  for 

nonsense  syllables  drops  very  rapidly  during  the  first  20  minutes 
after  learning.  More  than  half  of  the  original  material  is  lost  at 
the  end  of  the  first  hour.  The  subsequent  fall  of  the  curve  be¬ 
comes  less  and  less  abrupt  until  about  1  day,  when  the  curve 
runs  almost  parallel  to  the  abscissa.  Similar  but  far  less  ex¬ 
tensive  experiments  were  performed  upon  himself  with  meaning¬ 
ful  material,  i.  e.,  poetry.  From  these  results  Ebbinghaus  de¬ 
duced  the  following  equation  of  the  curve  which  has  remained 

a  classic  of  forty  years’  standing : 

100  k  b  k 

b  = - ,  or  -  = - 

(log  t)c  -|-k  100 — b  (log  t)c 

In  this  formula  b  —  percentage  of  retention,  100  —  b  =  per¬ 
centage  of  forgetting,  t  =  length  of  the  interval  in  no.  of  min., 
and  k  and  c  are  constants. 

With  Muller  and  Schumann,2  the  technique  was  greatly  im¬ 
proved  in  the  construction  and  the  presentation  of  the  syllable 
series.  Their  results  corroborated  those  of  Ebbinghaus,  though 
the  amount  of  forgetting  was  less  than  previously  reported. 

1  “Ueber  das  Gedachtniss :  Untersuchungen  zur  experimentellen  Psycholo¬ 
gic, ”  Leipzig,  1885.  Eng.  Tr.  by  Ruger  and  Bussenius,  Teachers’  College, 
Columbia  University,  1913. 

2  “Experimentelle  Beitrage  zur  Untersuchung  des  Gedachtnisses,”  Zeitschr. 
f.  Psychol.,  Vol.  VI,  1893. 


2 


C.  W.  LUH 


It  was  in  1903-04  that  Radossawljevitch3  attempted  a  more  care¬ 
ful  determination  of  the  curve  on  a  much  more  extensive  scale. 
He  employed  altogether  29  subjects,  as  against  Ebbinghaus’  one, 
who  was  himself.  Availing  himself  of  the  improved  technique  of 
Muller  and  Schumann,  he  further  introduced  accent  and  rhythm 
into  the  act  of  learning.  On  the  whole,  the  curve  he  described 
conforms  to  the  Ebbinghaus  type.  The  amounts  of  forgetting 
after  relatively  short  intervals  were  less  than  either  Ebbinghaus 
or  Muller  and  Schumann  discovered. 

Finkenbinder,4  who  re-attacked  the  problems  in  1912,  first 
used  the  anticipation  method  in  presentation.  By  that  method 
the  subject  was  required  to  anticipate  each  syllable  by  pronounc¬ 
ing  it  aloud  within  the  exposure  period  of  the  syllable  preceding. 
Successful  anticipation  of  the  whole  series  constitutes  the  stan¬ 
dard  of  learning.  Altogether  eleven  different  intervals  were  used, 
and  these  were  carefully  distributed  so  as  to  eliminate  diurnal 
variations.  He  summarized  his  data  as  follows :  “The  curve  of 
forgetting  for  nonsense  syllables  in  series  of  twelve,  as  determined 
by  the  lapse  of  time,  is  a  uniformly  progressive  curve  much  as 
Ebbinghaus  found,  but  under  the  conditions  of  our  investigation, 
the  progress  of  forgetting  is  slower  than  Ebbinghaus  found  it  to 
be,  but  somewhat  faster  than  Radossawljevitch  found. ”5  Then 
from  his  numerical  data  he  found  this  astonishingly  simple  equa¬ 
tion:  Forgetting  =  10  (log.  of  time  in  No.  of  min.  -f-  1),  and 
apologized  for  its  simplicity. 

In  the  above  quoted  investigations,  the  method  for  measuring 
the  amount  of  forgetting  was  the  relearning  or  “saving”  method. 
Forgetting  is  expressed  as  a  quotient  of  the  amount  of  time  for 
relearning  and  for  the  original  learning.  Strong6  first  undertook 

3  “Das  Behalten  und  Vergessen  bei  Kindern  und  Erwachsenen,”  Leipzig, 

1907. 

4  “The  Curve  of  Forgetting,”  Amer.  Jour.  Psychol.,  Vol.  XXIV,  1913. 

5  Ibid,  p.  32.  Finkenbinder  used  series  of  12  syllables  each ;  Ebbinghaus, 
13;  Radossawljevitch,  8,  12  and  16.  Finkenbinder  should  have  compared  his 
results  with  that  part  of  R’s  data  which  were  derived  from  12-syllable  series 
only. 

6  “The  Effect  of  Time  Interval  upon  Recognition  Memory,”  Psych.  Rev., 
Vol.  XX,  1913,  pp.  334  ff  . 


THE  CONDITIONS  OF  RETENTION 


3 


to  extend  the  investigation  with  other  methods  of  measuring  re¬ 
sults.  The  method  used  in  his  experiments  was  the  method  of 
recognition,  or  selection,  and  for  material  he  constructed  series 
of  common  English  words  of  40  each.  Out  of  each  40,  a  second 
series  of  20  words  was  drawn  at  random,  which  latter  served  as 
the  exposure  list.  The  first  list  of  40  was  given  the  subject  for 
recognition  after  the  lapse  of  a  designated  interval  of  time. 
From  these  the  subject  was  required  to  select  the  exposure  list. 
The  experiments  included  14  intervals  and  5  subjects,  but  only 
15  measures  for  each  interval.  The  curve  of  retention  thus  de¬ 
termined  was  similar  in  shape  to  that  of  Ebbinghaus.  The  two 
almost  agreed  as  to  actual  amounts  of  forgetting  until  after  the 
lapse  of  the  4-day  interval.  Strong,  therefore,  concluded  that 
“there  is  no  difference  in  the  form  of  the  curve  for  retention 
in  recall  and  recognition  memory/’  By  this  he  did  not  specify 
whether  he  implied  the  logarithmic  formula,  or  only  the  general 
shape  of  the  curve  as  to  its  initial  drop  and  negative  accelera¬ 
tion. 

Bean7  thought  that  the  Ebbinghaus  tradition  could  be  sub¬ 
stantiated  on  more  extensive  grounds.  In  his  experiments  two 
distinct  kinds  of  material  were  used,  ( 1 )  series  of  9  conso¬ 
nants  of  the  English  alphabet,  and  (2)  typewriting.  In  (1)  he 
used  two  methods  for  the  measurement  of  retention.  A.  The 
method  of  written  reproduction,  in  which  the  subjects  were  al¬ 
lowed  2  min.  to  reproduce  the  series  of  consonants  which  had 
been  learned  from  1  to  28  days  previous  to  recall.  B.  The 
method  of  selection  and  reconstruction,  in  which  the  subjects 
spent  90  secs,  in  selecting  the  original  series  of  9  out  of  the 
total  group  of  18  which  was  being  presented,  and  then  took  30 
secs,  to  put  the  original  9  in  the  right  order.  In  (2)  typewrit¬ 
ing,  Bean  adopted  a  method  similar  to  that  used  by  Book  in  his 
pioneering  studies  in  typewriting.8  Bean’s  results  may  be  sum¬ 
marized  as  follows  : 

The  curve  of  forgetting  may  be  studied  (1)  as  to  its  general 

7  “The  Curve  of  Forgetting,”  Archives  of  Psychol.,  Vol.  XX,  No.  3. 

8  “The  Psychology  of  Skill,”  Univ.  of  Montana  Publications  in  Psychology, 
Vol.  I,  1908,  Bull.  53,  Psy.  Series  No.  1. 


4 


C.  W.  LUH 


form;  and  (2)  as  to  the  absolute  rate  of  forgetting.  According 
to  him,  the  curves  he  presented  differ  from  those  of  earlier  in¬ 
vestigators  and  among  themselves,  not  in  general  form,  but  only 
in  absolute  initial  amount.  Supposing  the  logarithmic  type  of 
curve  to  be  general,  then  an  initial  high  amount  of  forgetting  will 
lead  to  apparently  abrupt  transitions.  As  to  the  cause  of  the 
variations  in  the  absolute  or  initial  amount,  numerous  conditions 
may  be  mentioned.  1.  Degree  of  learning.  2.  Distribution  or 
concentration  in  the  process  of  learning.  3.  Different  kinds  of 
material.  4.  Different  methods  by  which  retention  is  measured. 
5.  Individual  differences.  On  the  whole,  he  would  conclude  that 
all  curves  of  forgetting  are  logarithmic  curves. 

As  we  shall  later  develop,  the  methods  he  used  for  measuring 
the  amount  of  retention  were  mostly  crude  and  inaccurate.  He 
did  not  give  any  measurement  for  the  statistical  validity  of  his 
data.  Further,  he  himself  did  not  attempt  to  find  equations,  or 
rather  one  general  equation,  for  his  own  data,  and  we  have  to 
take  his  conclusions  only  as  pious  opinions.  Finally,  in  his  ex¬ 
periments,  none  of  the  conditions  he  mentioned  was  controlled 
and  independently  varied. 

An  even  more  sweeping  generalization  than  Bean’s  was  of¬ 
fered  by  Pieron.9  He  developed  a  formula  which  was  believed 
to  satisfy  all  the  conditions  of  immediate  and  permanent  memory, 
retention  and  forgetting,  muscular  contraction  and  the  phylo¬ 
genetic  development  of  retentive  phenomena,  etc.  That  formula 

k 

is  m  = - ,  where  m  =  percentage  of  “saving,”  t  = 

t"(logt)c 

length  of  the  interval,  and  k,  a  and  c  are  constants.  Then  putting 
a  =  o,  it  takes  in  Ebbinghaus’  curve  for  human  retention, 
k 

m  = - ,  as  a  congenial  member  of  the  “family.”10  But 

(log  t)c 

these  deductions  were  based  on  no  surer  foundation  than  a  few 
observations  upon  some  pond  snails. 

9  “L’fivolution  de  la  Memoire,”  Paris,  1910,  pp.  256-60. 

10  Notice  how  ingenuity  is  accentuated  by  forgetting  k  in  Ebbinghaus’  for¬ 
mula.  This  is  permissible  when  t  is  very  large.  But  E’s  formula  is  sig¬ 
nificant  only  when  it  is  small. 


THE  CONDITIONS  OF  RETENTION 


5 


All  the  above  writers  seem  to  concur  with  the  Ebbinghaus 
tradition  and  to  agree  on  these  points. 

(1)  Retention  decreases  with  time. 

(2)  Forgetting  is  more  rapid  at  first. 

(3)  The  curve  of  retention  is  generally  uniform  so  that  one 
can  state  it  in  terms  of  a  mathematical  formula.  Radossawlje- 
vitch  indeed  located  a  sudden  deviation  at  the  end  of  the  8  hr. 
interval,  but  that  was  smoothed  out  in  Finkenbinder’s  experi¬ 
ments  after  the  elimination  of  diurnal  variations. 

(4)  There  is  a  question  as  to  whether 

A.  The  curves  approximate  each  other  so  closely  that  one 
can  regard  them  as  being  chance  deviations  from  some  ideal 
curve,  or 

B.  They  belong  to  a  single  family  with  one  or  more  variable 
parameters  which  assume  different  values  according  to  different 
conditions.  Strong  inclines  toward  the  former  alternative,  but 
Bean  explicitly  favors  the  latter. 

It  is  to  be  noticed  that  conclusions  1  to  3  are  but  descriptive 
summary  statements  of  the  facts  as  observed  under  their  par¬ 
ticular  experimental  conditions,  while  4  is  a  mathematical  deduc¬ 
tion.  By  “the  Ebbinghaus  type  of  curve,”  one  may  simply  mean 
that  facts  can  be  so  described  and  graphically  represented,  with¬ 
out  implying  that  they  satisfy  any  kind  of  an  equation.  Neg¬ 
lecting  all  mathematical  complications,  may  not  the  phenomena 
of  retention  and  forgetting  be,  under  all  conditions ,  much  as 
Ebbinghaus  described  them? 


In  the  light  of  these  conclusions,  Ballard’s11  results  become 
significant.  He  experimented  on  school  children  with  Latin 
nouns,  nonsense  poetry,  geometric  diagrams,  nonsense  syllables, 
prose,  material  for  logical  memory,  but  above  all  with  ballad 
poetry.  For  the  vast  majority  of  his  subjects,  the  material  was 
not  completely  learned.  Written  reproduction  was  required 
after  the  lapse  of  a  certain  interval.  He  found  that  the  highest 
proficiency  of  retention,  as  measured  by  the  amount  of  repro- 

1:l“Obliviscence  and  Reminiscence,”  Brit.  Jour.  Psych.  Monograph  Supple¬ 
ments,  Vol.  I,  1913,  No.  2. 


6 


C.  W.  LUH 


duced  material,  was  reached  not  immediately  after  learning,  but, 
as  a  rule,  at  the  end  of  two  days.  The  graphs  in  Fig.  I  are  illus¬ 
trative.12  Both  A  and  B  are  curves  of  retention  for  children 
about  12  years  of  age.  The  amount  remembered  immediately 
after  learning  is  taken  as  the  basis  on  which  the  percentage  repro¬ 


duced  later  is  calculated.  Graph  A.  was  based  upon  “The  Wreck 
of  the  Hesperus,”  with  20%  of  the  material  remembered  in  the 
“primary  test.”  B.  was  based  upon  “The  Ancient  Mariner,” 
with  40%  of  the  material  remembered. 

These  results  of  Ballard  directly  contradict  every  one  of  the 
conclusions  reached  by  the  previous  writers.  Yet  his  data  seem 
to  be  at  least  as  valid  and  reliable  as  those  of  our  earlier  investi¬ 
gators  in  forgetting. 

This  apparent  dilemma  suggested  to  us  what  was,  in  a  way, 
anticipated  by  Bean.  When  the  conditions  of  learning  and  re¬ 
calling  are  changed,  not  only  will  the  “absolute”  amount  of  for¬ 
getting  change,  not  only  will  the  mathematical  formula  change, 
but  the  phenomenon  of  negative  acceleration  may  also  disap¬ 
pear.  The  conditions  under  which  Ballard  experimented  were 
greatly  different  from  those  of  other  investigators.  The  follow¬ 
ing  were  the  most  important : 

(1)  The  age  of  the  subjects.  Ballard’s  subjects  who  mani¬ 
fested  these  peculiarities  were  all  children.  Compared  with  his 
own  work  upon  adults,  the  results  indicate  that  the  curve  is  a 


12  Ibid,  p.  5. 


THE  CONDITIONS  OF  RETENTION 


7 


function  of  the  age  of  the  subjects.  Other  investigators  worked 
mostly  with  adults. 

(2)  The  kind  of  material.  Ballard  used  but  little  nonsense 
material  and  did  not  work  on  a  separate  curve  of  retention  for 
nonsense  syllables.  The  Ebbinghaus  type  of  curve  is  a  curve  for 
nonsense  syllables  par  excellence.  Ebbinghaus’  and  Radossawl- 
jevitch’s  experiments  with  meaningful  material  were  only  supple¬ 
mentary  to  their  principle  problem  and  were  haphazardly  per¬ 
formed. 

(3)  The  degree  of  learning.  In  Ballard’s  experiments,  the 
material  was  only  partly  learned.  The  degree  of  learning  for  the 
curves  quoted  above  was  20%  and  40%.  The  subjects  had  to 
stop  at  a  given  time  limit.  In  all  previous  work,  except  that  of 
Strong,  the  material  was  learned  at  least  to  the  first  errorless 
recitation. 

(4)  The  method  of  measuring  the  amount  of  retention.  Be¬ 
fore  Ballard,  the  method  that  was  generally  used  was  the  “sav¬ 
ing”  method.  Bean  and  Strong  tried  the  “selection”  method,  but 
not  very  extensively.  Ballard,  however,  found  the  written  repro¬ 
duction  method  to  be  more  suitable  for  group  experiments. 

This  comparison  suggests  the  question  as  to  whether  the  curve 
of  forgetting ,  or  of  retention ,  is  a  function  of  these  conditions ,  or 
more  specifically ,  whether  each  condition  determines  a  special 
curve.  The  present  study  is  an  attempt  to  answer  this  question. 
This  can  be  carried  out  only  by  varying  the  above  mentioned 
conditions  independently  and  systematically.  Unfortunately, 
Ballard’s  technique  has  necessitated  a  program  which  demands 
more  time  than  we  can  at  present  afford.  We  have,  therefore, 
limited  the  scope  of  the  problem  by  taking  up  only  the  third 
and  fourth  factors,  leaving  the  first  two  to  a  later  investigation. 

General  Description  of  the  Experiments 

The  experiments  were  performed  in  the  Psychological  Labora¬ 
tory  of  the  University  of  Chicago,  the  first  series  from  May  to 
August,  1919,  and  the  second  from  October,  1919,  to  February, 
1920. 


8 


C.  IV.  LUH 


(i)  Material 

Series  of  nonsense  syllables  of  12  each  were  used.  With 
the  English  alphabet,  a  list  was  made  of  all  possible  combina¬ 
tions  of  two  consonants  joined  by  a  vowel  in  the  middle,  except 
those  which  end  in  y.  From  this  list  we  eliminated  all  the  Eng¬ 
lish,  French,  German  and  Latin  words.  The  revised  collection 
was  then  submitted  separately  to  four  graduate  students  of  the 
department  who  checked  every  syllable  which  happened  to  call 
up  immediate  meaning  associations.  All  syllables  thus  marked 
out  by  more  than  one  of  the  observers  were  further  eliminated 
from  the  final  list. 

In  the  construction  of  the  series,  Muller’s13  rules  were  observed 
as  closely  as  possible.  That  is, 

( 1 )  All  the  initial  and  final  consonants  of  the  same  series  are 
different. 

(2)  Since  we  did  not  resort  to  the  use  of  diphthongs,  we  had 
five  vowels  as  against  Muller’s  twelve.  The  terms  were  arranged 
so  that  no  two  of  four  consecutive  syllables  have  the  same 
vowel. 

(3)  No  two  consecutive  syllables  have  any  consonant  in  com¬ 
mon. 

(4)  No  group  of  consecutive  syllables  constitutes  a  polysyl¬ 
labic  word  or  a  phrase. 

Thus  we  have  improved  upon  Muller  in  at  least  two  respects. 
( 1 )  He  overlooked  monosyllabic  words,  which,  perhaps,  is  not 
so  serious  an  omission  in  German  as  in  English.  (2)  While  he 
allowed  a  syllable  to  end  with  the  initial  consonant  of  the  pre¬ 
ceding  syllable,  we  excluded  all  such  cases. 

Since  in  our  investigation  we  required  the  subject  to  spell  each 
syllable  letter  by  letter,  instead  of  pronouncing  it  as  a  whole,  we 
are  no  longer  concerned  with  Gamble’s  rules14  which  were  for¬ 
mulated  as  safeguards  against  the  inherent  defects  of  English 
orthography.  We  also  think  that  spelling  the  syllable  letter  by 
letter  tends  to  minimize  its  meaning  associations. 

13  Op.  ext.,  p.  106. 

14  “A  Study  in  Memorising  by  the  Reconstruction  Method,”  Psych.  Rev., 
Monograph  Supplements,  Vol.  X,  No.  4,  p.  22. 


THE  CONDITIONS  OF  RETENTION 


9 


Altogether  about  90  series  were  constructed  so  that  a  subject 
could  serve  extensively  without  resorting  to  learning  a  single 
syllable  twice. 

(2)  Apparatus 

The  apparatus  was  an  ordinary  rotating  drum  used  in  the 
Chicago  laboratory  for  most  of  the  memory  experiments.  After 
the  series  were  typewritten  on  strips  of  white  manila  card,  they 
could  be  easily  fixed  to  the  drum.  One  syllable  was  exposed  at 
a  time  through  an  aperture  in  the  screen  attached  to  the  posts 
of  the  drum.  It  was  found  more  convenient  to  run  the  apparatus 
by  hand  than  by  a  mechanical  device,  since  the  experimenter  had 
to  keep  his  eyes  on  the  aperture  in  order  to  be  perfectly  sure 
that  the  subject  spelled  the  syllable  completely  before  the  suc¬ 
ceeding  one  was  exposed. 

In  experiments  like  these,  every  moderately  loud  noise  may 
be  disturbing.  For  this  reason  the  experimenter  had  to  keep  the 
time  by  running  a  telephone  wire  from  an  adjacent  room  in  which 
a  metronome  was  set  at  two  seconds. 

In  the  later  part  of  the  first  series  of  experiments  and  through¬ 
out  the  second,  it  was  thought  worth  while  for  purposes  other 
than  that  of  the  present  study  to  keep  minute  records  of  every 
correct  or  incorrect  response.  A  Remington  typewriter  No.  6, 
invisible,  served  as  the  apparatus,  so  that  the  subject  would  not  be 
distracted  by  what  was  being  recorded.  Two  keys  were  arbi¬ 
trarily  chosen  to  mark  success  and  failure.  The  striking  of  the 
key  made  a  noise  every  two  seconds.  The  effect  of  this  appar¬ 
ently  disturbing  factor  was  inappreciable,  so  far  as  we  can  de¬ 
termine  from  the  practice  curves  of  the  individuals. 

(3)  Method  of  Presentation 

The  subject  was  seated  at  a  convenient  distance  in  front  of  the 
rotating  drum.  Before  the  presentation  of  every  new  series,  the 
experimenter  gave  the  signal  “ready,”  one  second  after  which 
the  first  syllable  was  exposed.  This  signal  became  superfluous 
after  one  or  two  weeks  of  practice.  The  time  of  exposure  for 
each  syllable  was  2  secs.  No  restriction  was  made  as  to  the 


IO 


C.  W.  LUH 


method  of  learning,  excepting  that  the  subject  was  warned  not 
to  form  artificial  meaning  associations.  Beginning  with  the 
second  exposure  of  the  series,  he  was  instructed  to  attempt  to 
anticipate  each  syllable  by  spelling  it  aloud  before  it  was  exposed. 
Usually  6  seconds  were  allowed  between  successive  presenta¬ 
tions  of  a  series,  during  which  the  experimenter  shifted  the  drum 
and  made  the  necessary  records.  A  series  was  considered  learned 
once  the  subject  successfully  anticipated  every  syllable.  All 
series  were  learned  by  successive  presentations  in  a  single  sitting. 

Each  subject  was  required  to  return  at  the  same  time  of  the 
day,  but  could  skip  two  or  three  days  in  succession  between 
series.  Only  one  series  was  learned  in  a  day.  Occas  onally 
the  learning  of  a  new  series  followed  immediately  after  the  recall 
of  the  preceding  one.  But  this  never  happened  in  the  second 
series  of  experiments. 

The  different  intervals  and  the  methods  of  measurement,  as 
will  be  described  later,  were  distributed  according  to  a  tentative 
scheme  drawn  for  each  subject.  Somet’mes  that  schedule  had 
to  be  slightly  changed,  but  care  was  always  taken  to  reduce  to  a 
minimum  the  effect  of  uncontrolled  practice. 

Each  subject  was  given  4-6  series  for  preliminary  practice. 
These  results  were  not  counted.  (Subject  C,  who  learned  only 
20  series,  began  to  work  late  in  the  summer.  Onlv  2  p  actice 
series  were  possible  with  this  subject.  His  results  could  have  been 
improved  by  giving  2  or  more  additional  preliminary  series). 

(4)  Subjects 

Ten  subjects  a  day  were  all  we  could  handle.  We  had  two 
groups  of  ten  each.  The  first  group  included  one  instructor  and 
three  graduate  students  of  the  department  and  six  Chinese  stu¬ 
dents  of  the  University  who  had  one  time  or  another  taken  some 
work  in  psychology.  In  the  second  group,  there  were  six  gradu¬ 
ate  students  and  one  senior  of  the  department,  including  the  ex¬ 
perimenter.  The  other  three  were  Chinese  students  of  the  Uni¬ 
versity,  two  of  whom  never  had  any  work  in  psychology.  Sub¬ 
ject  Y,  a  Chinese  student  who  learned  20  series  in  the  summer, 
served  again  as  one  of  the  ten.  When  the  experimenter  served 


THE  CONDITIONS  OF  RETENTION 


ii 


as  subject,  the  series  were  given  by  Mr.  T.  L.  Wang,  who  had 
also  served  in  previous  experiments.  In  this  case,  the  series  were 
made  according  to  rules  unknown  to  the  experimenter.  They 
were  very  similar  to  the  ordinary  ones. 

Apparently  the  Chinese  students  had  no  serious  difficulty  in 
learning  this  type  of  material.  They  were  able  to  memorize 
directly  without  translating  the  exposed  material  into  Chinese 
equivalents.  On  the  whole,  they  learned  the  series  very  much 
faster  than  did  the  Americans. 


II.  THE  AMOUNT  OF  RETENTION  AS  A  FUNCTION 
OF  THE  METHOD  OF  MEASUREMENT 


In  the  first  series  of  experiments,  two  methods  of  recall  were 
used,  which  together  furnished  five  measurements  of  the  amount 
of  retention. 

1.  The  Anticipation  and  Relearning  Methods.  In  one  half  of 
the  series  given  to  each  subject,  the  method  of  presentation  in 
relearning  was  identical  with  that  of  the  original  learning. 

(A)  Thus,  the  subject  was  required  to  anticipate  the  series 
at  the  very  first  presentation,  at  the  rate  of  2  sec.  for  each  syl¬ 
lable.  The  number  of  correct  syllables  was  recorded.  That 
number,  expressed  as  a  percentage  of  the  whole  series,  established 
a  measurement  of  retention  in  terms  of  anticipatory  recall. 

(B)  After  the  first  record  was  taken,  the  series  was  exposed 
as  many  times  as  necessary  for  complete  relearning.  A  measure¬ 
ment  of  retention  was  thus  furnished  by  the  “Saving  Method.” 

2.  The  Reproduction,  Recognition  and  Reconstruction 
Methods.  These  methods  were  used  with  the  other  half  of  the 
series  given  to  each  subject. 

(C)  The  subject  was  first  furnished  with  a  recall  blank,  on 
which  were  three  columns  of  figures  from  1  to  12,  each  with  a 
blank  space  to  the  right.  He  was  instructed  to  write  down  the 
original  series  in  the  right  spatial  order,  beginning  with  the  left 
hand  column,  but  not  necessarily  in  the  same  temporal  order  as 
the  series  was  learned.  At  the  end  of  1  min.  the  experimenter 
gave  a  signal,  at  which  the  subject  began  to  write  in  the  middle 
column,  filling  out  spaces  that  had  been  left  open  during  the  first 
minute,  or  correcting  any  mistake  that  he  thought  had  been 
made.  Another  signal  was  given  at  the  end  of  the  second 
minute.  At  this,  the  subject  changed  to  the  right  hand  column. 
Three  more  minutes  were  allowed  for  further  reproduction  and 
correction.  The  subject  could,  of  course,  “give  up”  at  any  time, 
or  finish  the  whole  series  before  the  lapse  of  the  first  or  second 


12 


THE  CONDITIONS  OF  RETENTION 


13 


minute.  A  time  record  was  also  taken  for  each  series  completed 
within  the  above  5  min.  This  constituted  a  measurement  of  re¬ 
tention  by  the  Written  Reproduction  method. 

(D)  Immediately  following  upon  written  reproduction,  a 
group  of  24  syllables  was  given  the  subject,  out  of  which  he  was 
required  to  select  the  original  12,  no  more  and  no  less.  At  the 
end  of  90  sec.  the  experimenter  quietly  took  a  record  of  the 
number  of  correct  and  incorrect  syllables  selected  up  to  that 
time.  A  similar  record  was  taken  when  the  subject  completed 
the  selection  of  12  syllables,  correctly  or  incorrectly,  together 
with  a  time  record.  The  time  limit,  90  sec.,  was  determined  from 
the  averages  of  the  preliminary  records  of  all  the  subjects  in  the 
first  series  of  experiments.  This  process  gave  a  measurement 
of  retention  in  terms  of  Recognition. 

(E)  Finally,  the  subject  was  furnished  with  the  original  12 
syllables  on  separate  slips  of  white  manila  card  and  was  required 
to  reconstruct  the  order  of  the  series.  The  actual  order  of  recon¬ 
struction  was  recorded,  and  also  the  amount  of  time  spent  in  the 
reconstruction  process.  This  we  may  call  the  Reconstruction  or 
Rearrangement  method  of  recall. 

Intervals  of  Time 

Five  intervals  of  time,  i.  e.,  20  min.,  1  hr.,  4  hrs.,  1  day,  and  2 
days,  were  selected  with  two  considerations  in  view. 

(1)  To  facilitate  comparison  with  earlier  reports,  it  was  nec¬ 
essary  to  fix  our  program  into  that  of  other  investigators.  Ac¬ 
cordingly,  intervals  which  had  not  been  included  in  the  work  of 
one  or  more  of  our  predecessors  do  not  appear  in  our  plan.  We 
further  took  into  consideration  whether  the  points  on  the  curve 
to  be  thus  empirically  determined  would  be  likely  to  represent 
an  equation,  if  there  be  one.  Cf.  Table  VII. 

(2)  We  also  tried  to  avoid  the  effect  of  diurnal  variations. 
Later  we  found  that  the  4  hr.  interval  was  too  long  for  our  pur¬ 
pose.  Any  interval  longer  than  4  hrs.  and  shorter  than  24  would 
be  too  much  beyond  our  control. 


14 


C.  W.  LUH 


Methods  of  Scoring 

(1)  Anticipation.  With  this  method  complete  retention  is 
the  successful  anticipation  of  every  syllable.  There  are  12  syl¬ 
lables  in  each  series.  On  the  basis  of  12  one  can  easily  convert 
an  actual  score  into  percentage  terms. 

(2)  Relearning.  The  usual  “saving  method”  was  used,  in 
which  the  number  of  presentations  in  relearning  minus  one,  di¬ 
vided  by  the  number  of  presentations  in  learning  minus  one,  mul¬ 
tiplied  by  100,  gives  the  percentage  of  forgetting. 

(3)  Written  Reproduction.  First,  the  reproduced  amount  is 
compared  with  the  possible  amount.  X  correct  syllables  repro¬ 
duced  is  scored  at  X/12,  which,  multiplied  by  100,  gives  a  per¬ 
centage  score.  A  syllable  with  only  2  letters  correct  is  scored 
J4,  as  is  also  one  with  the  initial  and  final  consonants  inverted. 

Secondly,  we  took  into  consideration  the  position  and  sequence 
of  each  reproduced  syllable.  The  difficulties  for  such  minute 
scoring  are  two.  (1)  The  relative  value  of  the  reproduced 
amount  on  the  one  hand  and  of  position  and  sequence  on  the 
other  can  only  be  arbitrarily  determined.  (2)  By  chance  the 
subject  may  reproduce  a  certain  number  of  syllables  in  the 
original  position  or  sequence  without  actually  remembering 
either,  and  it  is  well  nigh  impossible  to  score  this  chance  factor. 
In  the  present  study,  the  total  amount  of  reproduced  material 
will  be  roughly  scored  J4,  and  position  and  sequence  %  each. 
It  is  assumed  that  material  contributes  as  much  value  as  position 
and  sequence  put  together,  and  the  latter  are  again  considered 
to  be  equal  in  value.  The  chance  factor  is  neglected.  The  records 
are,  therefore,  scored  too  high,  but  the  extent  of  this  effect  one 
can  easily  approximate  when  we  come  to  deal  with  the  method 
of  scoring  reconstruction.  Any  such  arbitrary  process  will,  of 
course  incur  all  the  criticism  that  has  been  heaped  upon  Lyon1 
by  writers  like  Kjerstad.2  The  latter,  however,  also  neglected 
the  chance  factor.  Our  interpretations  will  be  based  mainly  upon 

1  “A  Rapid  and  Accurate  Method  for  Scoring  Nonsense  Syllables  and 
Words,”  Amer.  Jour.  Psychol.,  Vol.  XXIV,  1913,  pp.  525-31. 

2  “The  Form  of  the  Learning  Curves  for  Memory,”  Psych.  Rev.,  Monograph 
Supplements,  Vol.  XXVI,  1919,  No.  5,  pp.  14  ff. 


THE  CONDITIONS  OF  RETENTION 


15 


the  first  method  of  scoring,  which  does  not  take  into  account  po¬ 
sition  and  sequence. 

Further,  unlike  the  other  methods  of  scoring,  the  values  for 
written  reproduction  are  independent  of  the  amount  of  error 
made  in  recalling.  The  amount  of  error  may  also  be  reduced  to 
percentage  scores  when  compared  with  the  actual  or  the  possible 
amount  of  retention,  i.  e.,  the  amount  of  error  may  be  computed 
as  a  percentage  either  of  the  whole  series  or  of  the  reproduced 
material  only. 

(4)  Recognition.  When  a  number  of  syllables  originally 
learned  are  mixed  up  with  an  equal  number  of  new  ones  and  then 
presented  to  the  subject  for  recognition,  the  outstanding  fact  is 
that,  by  pure  chance,  one  will  most  probably  draw  half  of  the 
original  ones.  Bean3  overlooked  this  difficulty.  Consequently, 
all  his  values  were  above  50%  even  to  the  end  of  the  28th  day. 

To  eliminate  this  chance  factor,  Strong4  devised  the  formula, 

Correct  recognitions  Correct  —  incorrect  recognitions 
Retention  = - X  - X  too. 

Total  no.  presented  Correct  -f~  incorrect  recognitions 

No  doubt,  this  formula  takes  into  account  the  extremes  of  proba¬ 
bility.  That  is,  out  of  X  things  learned,  a  recognition  of  X/2  is 
scored  o,  while  a  recognition  of  X  is  scored  100.  Beyond  that, 
the  formula  is  exposed  to  numerous  difficulties  and  seems  to  de¬ 
feat  its  own  purpose.  The  author  pointed  out  that  “it  penalizes 
mistakes  a  little  more  than  is  warranted  on  a  basis  of  chance.” 
As  a  matter  of  fact,  it  penalizes  sometimes  too  much  and  some¬ 
times  too  little.  In  other  words,  the  scores  given  on  this  basis 
are  not  always  proportional  to  the  probability.  That  propor¬ 
tionality,  it  seems  to  me,  ought  to  be  the  criterion  for  the  validity 

g  g j 

of  the  formula.  For  instance, -  X  tt-; - X  100  =  25.9%. 

24  8+1 

Similarly,  8  correct  ones  and  2  incorrect  ones  would  be  scored 
20.0%,  and  8  correct  ones  and  3  incorrect  ones  15.6%.  Now 

*op.  cit.  His  reproduction  method  is  not  any  better.  When  one  is  re¬ 
quired  to  write  down  9  out  of  18  consonants  it  is  most  probable  that  4  or  5 
will  be  correct,  even  though  one  does  not  realize  there  are  only  18  consonants 
in  the  English  alphabet. 

4  Op.  cit .  p.  355.  Cf.  Psych.  Rev.,  Vol.  XIX,  pp.  457  ff. 


i6 


C.  W.  LUH 


when  24  members  are  presented,  the  respective  probabilities  for 

945  3465  9075 

these  three  combinations  to  occur  are -  : -  : - , 

52003  52°03  52003 

provided  that,  by  pure  chance,  one  is  as  likely  to  take  9  as  10  or 
11.  It  is  very  difficult  to  see  how  the  chance  factor  is  counter¬ 
balanced  by  giving  scores  such  as  the  above. 

Again,  suppose  that  of  the  total  group  presented,  the  subject 
selects  only  1  and  that  1  be  correct.  According  to  the  formula, 

1  1  — o 

this  performance  would  be  scored -  X - X  100. 

Total  no.  1  +  o 

But  if  in  the  total  number  presented,  the  number  of  original  ones 
is  equal  to  the  number  of  new  ones,  the  subject  will  be  just  as 
likely  to  draw  a  correct  one  as  an  incorrect  one.  Such  a  per¬ 
formance  should  be  scored  o. 

Other  defects  of  the  formula,  while  not  inherent  and  unavoid¬ 
able,  result  from  assumptions  which  one  makes  in  applying  it. 
Thus  Strong  required  his  subjects  to  classify  their  judgments 
according  to  degrees  of  certainty.  After  the  first  class,  i.  e., 
the  most  certain  one,  is  scored  by  his  formula,  the  second  and 
third  classes  cannot  be  penalized  as  rigidly,  since  chance  has 
been  greatly  reduced  by  the  exclusion  of  the  correct  ones  in  the 
first  class. 

Further,  on  the  basis  of  the  first  class  as  1,  Strong  scored  the 
second  class  ^4,  and  the  third  class  *4-  These  values  are  en¬ 
tirely  arbitrary  and  have  nothing  to  do  with  the  formula.  But 
this  method  of  scoring,  together  with  the  last  named  oversight, 
certainly  helped  to  make  his  curve  of  recognition  memory  some¬ 
thing  like  Ebbinghaus’  curve. 

In  the  formulation  of  our  own  method  of  scoring,  we  first 
take  it  for  granted  that,  if  there  were  no  chance  factor,  each 
score  should  then  increase  upon  the  next  by  a  constant  amount. 

Then  we  calculated  the  probability  of  each  kind  of  combination. 
Thus,  when  the  total  group  of  24  is  presented,  there  are  2704156 
possible  ways  to  take  12.  These  are  classified  as  follows: 


THE  CONDITIONS  OF  RETENTION 


i.7 


No.  in  which  there 

are  12  correct 

and  0  incorrect, 

1 

11 

1 

144 

. 

10 

2 

4356 

9 

3 

48400 

8 

4 

245025 

7 

5 

627264 

6 

6 

853776 

etc. 

Six  correct  is  the  highest  probability,  the  combination  which  is 

most  likely  to  occur  on 

the  basis  of 

pure  chance. 

If  we  next 

regard  this  probability  as 

100%  chance,  we  have 

6  correct  and  6  incorrect, 

100.00%  chance, 

7 

5 

73-47% 

8 

4 

28.70% 

9 

3 

5.67% 

10 

2 

.51% 

11 

I 

.02% 

12 

0 

.00% 

Everything  below  6  correct  may  be  disregarded.  Now  divide 
ioo  into  6  equal  intervals,  from  6  to  12,  for  scores  when  the 
chance  factor  is  not  deducted.  Deducting  from  each  interval  the 
relative  amount  of  chance,  the  final  scale  is 

TABLE  I 


CORRECT 

INCORRECT 

PRELIMINARY  SCORE 

CHANCE 

FINAL 

6 

6 

0.00 

100.00 

0.00 

7 

5 

16.67 

73-47 

4.42 

8 

4 

33-33 

28.70 

23-76 

9 

3 

50.00 

5.67 

47-17 

10 

2 

66.67 

•51 

66.33 

11 

1 

83-33 

.02 

83-31 

12 

0 

100.00 

.OO 

100.00 

By  extending  this  method,  we  can  score  recognition  (i)  for 
any  number  of  things  presented,  (2)  for  any  number  selected 
( not  necessarily  one-half  of  the  number  presented) ,  and  (3)  for 
any  number  of  correct  or  incorrect  things  selected.  This  may  be 
seen  from  Table  II,  which  can  be  extended  indefinitely.  In  scor¬ 
ing,  we  can  make  use  of  this  table  and  save  a  tremendous  amount 
of  time. 

One  must  remember  that  these  values  are  the  most  probable 
values.  That  is,  in  the  long  run,  they  will  measure  actual  ef¬ 
ficiency.  Another  method,  and  a  more  logical  one,  to  score  proba- 


i8 


C.  W.  LUH 


bility  is  to  take,  for  instance,  a  performance  of  X  correct  choices 
and  12  —  X  incorrect  ones,  and  see  how  probably  that  perform¬ 
ance  would  happen,  supposing  the  subject  actually  knows  only 
i,  2  or  any  number  of  the  correct  things  selected.  Score  the 
number  that  the  subject  is  supposed  to  know  in  order  to  make 
such  a  performance  most  probable. 

However,  this  method  does  not  serve  our  purpose,  because 
it  sometimes  gives  ambiguous  results.  For  example,  if  a  per¬ 
formance  is  9  correct  to  3  incorrect,  we  do  not  know  whether 
the  subject  should  be  credited  with  8  or  9  which  he  is  supposed 
to  remember.  For 


Supposing  he  knows  9,  then  the  Supposing  he  knows  8,  then  the 


probability  for  him  to  get 
9  correct  is . 220/455 

10  “  “ . 198/455 

11  “  “ .  36/455 

12  “  “ .  1/455 


probability  for  him  to  get 

8  correct  is . 495/1820 

9  “  “ . 880/1820 

10  “  “ . 396/1820 

11  “  “ .  48/1820 

12  “  “ .  1/1820 


But  the  highest  probability  of  the  first  column  is  equal  to  that 
of  the  second  column. 


220  880 


455  1820 

Shall  the  subject  be  credited  8  or  9? 


TABLE  II 


Table  for  Scoring  Recognition  Memory,  24  presented, 
12  correct  12  incorrect 


NO. 


NO.  SELECTED 


CORRECT  I 

1  00.00 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 


23456  7  8  9  10  11  12 

00.00  00.00  00.00  00.00  00.00  00.00  00.00  00.00  00.00  00.00  00.00 

09.03  00.00  00.00  00.00  00.00  00.00  00.00  00.00  00.00  00.00  00.00 

18.06  06.57  00.00  00.00  00.00  00.00  00.00  00.00  00.00  00.00 

29.54  12.31  05.42  00.00  00.00  00.00  00.00  00.00  00.00 

39.40  26.78  10.11  04.82  00.00  00.00  00.00  00.00 

49-05  34-93  25.03  09.03  04.52  00.00  00.00 

57.82  48.06  32.40  24.07  08.51  04.42 

66.52  55.39  47.40  31.21  23.76 

74.96  66.39  53-91  47-17 
83-32  73-25  66.33 
91.67  83.31 
100.00 


THE  CONDITIONS  OF  RETENTION 


19 


(5)  Reconstruction.  In  this  method,  we  encountered  the  same 
difficulty  of  chance  success,  and  so  far  as  we  know,  no  attempt 
was  made  to  eliminate  this  factor  in  previous  studies.  We  first 
divide  our  problem  into  (A)  position  and  (B)  sequence.  It  is 
evident  that,  by  chance,  one  may  put  a  part  of  the  series  in  the 
original  position  and  sequence. 

(A)  Take  position  first.  Assuming  perfect  chance  in  the  re¬ 
arrangement  of  n  things,  the  number  of  ways  for  X  of  the  n 
things  to  be  out  of  the  original  order  is  the  number  of  n  things 
taken  X  at  a  time,  minus  the  number  of  permutations  of  X 
things  in  which  the  X  things  are  not  all  out  of  the  original  posi¬ 
tions.  For  12  things,  the  probability  for  any  number  of  them  to 
be  out  of  position  as  compared  with  any  other  number,  is 

o  positions  out,  1 

2  66 

3  440 

4  4455 

5  34848 

6  244860 

7  1468368 

8  7342335 

9  29369120 

10  88107426 

11  176214840 

12  176214841 


479001600 

Taking  17621841  as  100%  chance  and  following  the  same  pro¬ 
cedure  as  in  the  recognition  method,  we  have  the  results  as  given 
in  Table  III. 

TABLE  III 


POSITIONS  OUT 

PRELIMINARY  SCORE 

CHANCE 

FINAL  SCORE 

12 

00.00 

100.00 

00.00 

II 

09.09 

100.00 

00.00 

10 

I8.l8 

50.00 

O9.O9 

9 

27.27 

16.67 

22.72 

8 

36.36 

4.17 

34-84 

7 

4545 

•83 

45.07 

6 

54-55 

.14 

5447 

5 

63.64 

.02 

63.63 

4 

72.73 

.OO 

72.73 

3 

81.82 

.OO 

81.82 

2 

90.91 

.00 

90.91 

0 

100.00 

.00 

100.00 

20 


C.  W.  LUH 


The  principle  applied  in  the  development  of  this  scale  is  not 
limited  to  a  series  of  any  particular  number. 

(B)  Sequence.  Here  we  failed  to  formulate  a  simple  mathe¬ 
matical  statement  of  the  relative  amounts  of  chance  and  had  to 
depend  upon  empirical  data.  By  casting  a  series  of  12  members 
1000  times  and  recording  the  chance  sequences  of  the  members, 
we  obtained  the  results  given  in  Table  IV, 


TABLE  IV 

MEMBERS  OUT  OF  ORIGINAL  SEQUENCE 


I 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

1st  100  trials 

0 

O 

0 

0 

0 

0 

1 

5 

15 

42 

37 

100 

2nd 

0 

0 

0 

0 

0 

1 

0 

4 

13 

4i 

4i 

100 

3d 

0 

0 

0 

0 

0 

0 

2 

5 

10 

35 

48 

100 

4th 

0 

0 

0 

0 

0 

0 

1 

4 

19 

34 

42 

100 

5th 

0 

0 

0 

0 

0 

0 

0 

4 

14 

45 

37 

100 

6th 

0 

0 

0 

0 

0 

0 

1 

5 

20 

32 

42 

100 

7th 

0 

0 

0 

0 

0 

0 

1 

3 

18 

37 

4i 

100 

8th 

0 

0 

0 

0 

1 

0 

0 

4 

12 

37 

46 

100 

9th 

0 

0 

0 

0 

0 

1 

1 

3 

18 

33 

44 

100 

10th 

0 

0 

0 

0 

0 

0 

1 

3 

13 

36 

47 

100 

0 

0 

0 

0 

1 

2 

8 

40 

152 

372 

425 

1000 

Comparing  the  totals  with  each  of  the  10  groups,  we  concluded 
that  these  results  were  regular  enough  to  be  a  valid  sample.  We 
then  followed  exactly  the  same  procedure  as  in  the  scoring  of 
position  and  obtained  the  final  scale  as  given  in  Table  V. 

TABLE  V 


o  out  of  sequence, 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 


Score  100.00 
90.91 
81.82 
72.73 
63.64 

54-42 

45.24 

35-68 

24.70 
11.68 
1. 13 
.00 


(C)  After  scoring  both  position  and  sequence,  the  average  of 
the  two  was  taken  as  a  rough  measurement  of  Reconstruction 


THE  CONDITIONS  OF  RETENTION 


21 


memory.  This  final  process  is  arbitrary  and  may  be  entirely 
superfluous.  It  does  not  furnish  any  more  adequate  measure¬ 
ment  of  reconstruction  than  position  and  sequence  taken  sepa¬ 
rately,  since  the  resulting  values  do  not  lend  themselves  to  a 
clearer  interpretation. 

Quantitative  Data 

The  results  from  these  five  methods  of  measurement  are 
tabulated  in  Table  VI  and  graphically  represented  in  Fig.  II. 

TABLE  VI 

Percentage  of  Retention 

20  min.  i  hr.  4  hrs.  1  day  2  days 


Anticipation*  .  67.8  50.2  39.0  17.8  10.0 

Relearning*  .  75.0  65.9  54-9  52. 1  477 

Written  reproduction .  88.1  82.1  60.5  39.2  26.7 

Reconstruction  .  91.5  89.7  75.4  50.9  38.6 

Recognition  .  97.8  94.6  93.3  74.6  71.5 


From  Table  VI  and  Fig.  II,  the  phenomena  of  retention  may 
be  generally  stated  as  follows : 

(1)  The  amount  of  retention  decreases  with  time. 

(2)  On  the  whole,  forgetting  is  most  rapid  at  first,  but  there 
are  two  notable  exceptions.  A.  The  curve  for  recognition  slopes 
down  much  more  rapidly  from  4  hrs.  to  1  day  than  from  1  to 
4  hrs.  B.  In  reconstruction,  the  decrease  in  the  amount  of  re¬ 
tention  is  more  rapid  from  1  hr.  to  4  hrs.  than  from  20  min.  to 
1  hr. 

(3)  All  the  curves  are  relatively  uniform  and  can  be  described 
by  mathematical  formulae. 

*In  the  latter  part  of  this  series  of  experiments,  it  was  found  necessary 
to  counteract  the  effect  of  diurnal  variations  by  distributing  the  4-hr.  series 
more  carefully.  Some  of  these  series  were  given  at  the  regular  learning 
time  of  the  day  for  each  subject;  the  rest  were  given  either  4  hrs.  before  or 
after  that  time.  This  procedure  was  carried  out  only  for  anticipation  and 
relearning.  Subject  K’s  records  were  excluded  from  the  above  averages 
for  not  being  so  distributed. 

Because  of  a  mistake  in  scoring,  subject  D’s  5  records  had  to  be  excluded 
from  the  averages  for  anticipation. 

Altogether,  the  averages  for  anticipation  represent  28  records  from  8 
subjects;  relearning  represents  33  records  from  9  subjects;  the  rest  include 
35  records  from  10  subjects. 


22 


C.  W.  LUH 


(4)  Four  of  the  curves  stand  invariably  in  a  given  order. 
Recognition  gives  the  highest  values.  Reconstruction  occupies 
the  second  position.  Written  reproduction  follows  as  a  close 
third.  Anticipation  always  has  the  lowest  value. 

(5)  The  relation  of  the  values  for  relearning  varies  with  the 
time  interval.  As  may  be  seen,  its  order  is  fourth  for  the  20- 
min.  interval  and  second  for  the  2-day  interval. 

In  general,  these  conclusions  are  in  harmony  with  the  results 
of  earlier  investigations,  except  those  of  Ballard.  These  results 
are  brought  together  in  Table  VII  and  compared  with  those  of 
the  present  study. 

In  relearning,  the  present  results  approach  most  closely  to 
those  of  Finkenbinder.  In  no  instance  is  the  difference  more 
than  10%.  Finkenbinder  used  practically  the  same  technique 
as  our  own,  excepting  that  we  required  the  subject  to  spell  the 
syllable  instead  of  pronouncing  it  as  a  whole. 

With  the  “saving  method,”  an  increase  in  the  number  of  pres¬ 
entations  in  learning  increases  the  amount  of  retention,  while 
an  increase  in  the  number  of  presentations  in  relearning  de¬ 
creases  the  same.  Since  the  number  of  presentations  in  relearn¬ 
ing  is  almost  always  smaller  than  that  of  learning  (except  in  cases 
of  100%  forgetting),  every  increase  of  equal  or  nearly  equal 
magnitude  in  the  number  of  presentations  in  both  learning  and 
relearning  will  increase  the  amount  of  forgetting,  or,  in  other 
words,  it  decreases  the  amount  of  retention  thus  calculated. 


THE  CONDITIONS  OF  RETENTION 


23 


TABLE  VII 

Relearning  Recognition 


INTERVALS 

EBBING.  RADOSSAWLJEVITCH 

FINK. 

LUH 

STRONG 

LUH 

15  sec. 

* 

84.6 

5  min. 

97-5 

95-9 

727 

15  min. 

62.7 

97-8 

20  min. 

58.2 

88.6 

89.8 

75-0 

30  min. 

75-o 

55-5 

94.6 

I  hr. 

44.2 

70.7 

75-3 

72.8 

65.9 

57-3 

94.6 

2  hrs. 

69.4 

47.2 

93-3 

4  hrs. 

64.4 

54.9 

50.6 

93-3 

8  hrs. 

35-8 

474 

66.5 

65.5 

40.6 

12  hrs. 

63.8 

41. 1 

16  hrs. 

63.0 

24  hrs. 

337 

68.9 

70.2 

57-8 

52.1 

28.8 

74-6 

36  hrs. 

58.8 

2  days 

27.8 

60.9 

72.3 

55-6 

477 

22.9 

71.5 

3  days 

52.1 

4  days 

19.3 

6  days 

25.4 

49-3 

59.5 

7  days 

9.6 

14  days 

41.0 

51.4 

21  days 

37-8 

48.6 

30  days 

21.1 

20.2 

27.0 

42  days 

6-3 

120  days 

2.8 

3-3 

*  Averages  reconstructed  from  R’s  principal  experiments  which  included 
only  series  of  12  syllables.  The  column  immediately  to  the  left,  as  quoted  by 
F.,  represents  averages  from  8,  12  and  16  syllable  series. 


Other  things  being  equal,  it  takes  a  subject  more  presentations 
to  spell  a  series  correctly  than  to  pronounce  it  correctly,  both  in 
learning  and  relearning.  This  may  explain  the  fact  that  the 
relearning  values  reported  in  the  present  study  are  lower  than 
those  of  Finkenbinder. 

Similarity  of  technique  does  result  in  proportional  similarity 
of  quantitative  data.  It  points  toward  the  possibility  of  estab¬ 
lishing  norms,  though  not  one  norm  or  one  general  curve  of 
forgetting,  for  various  conditions  of  retention.  Other  numerical 
differences  between  the  present  study  and  previous  reports  may 
be  easily  accounted  for  by  individual  differences  and  the  disparity 
of  methods. 

The  difference  between  our  recognition  values  and  Strong’s  is 


24 


C.  W.  LUH 


sometimes  as  high  as  50%.  There  is  no  cause  for  wonder,  how¬ 
ever,  since  the  data  were  collected  under  as  divergent  conditions 
as  imaginable.  The  material,  the  degree  of  learning  and  the 
methods  of  scoring  were  all  different.  Our  data  will  have  to  be 
distorted  a  great  deal  before  they  can  conform  to  the  Ebbing- 
haus  type  of  curve.  Even  if  we  could  derive  a  general  equation 
which  satisfies  both  sets  of  values,  it  would  be  so  complex  and 
obscure  that  scientific  interpretation  would  be  better  off  without 
it.  Here  lies  the  danger  of  speculation  without  specifying  the 
conditions  and  variables  which  enter  into  the  determination  of 
our  values. 


Miscellaneous  Comparisons 

1.  The  Difference  between  Scoring  the  Number  of  Syllables 
and  of  Letters  in  Anticipation. 

There  are  altogether  12  syllables,  or  36  letters,  in  each  syllable 
series.  Since  a  syllable  may  be  only  partly  anticipated,  i.  e.} 
when  only  one  or  two  letters  of  the  syllables  are  anticipated  in 
the  correct  position  and  sequence,  it  is  evident  that  scoring  the 
number  of  letters  will  give  higher  values  than  scoring  the  num¬ 
ber  of  syllables.  The  increment  is,  however,  very  small,  as  can  be 
seen  from  Table  VIII. 


TABLE  VIII 


29.min. 

I  hr. 

2  hrs. 

1  day 

2  days 

Anticipation,  scoring  12  syllables 

67.8 

50.2 

39-0 

17.8 

10.0 

36  letters 

70.2 

54-2 

41.6 

19.7 

10.5 

That  there  is  a  positive  difference  at  each  interval  in  favor  of 
the  number  of  letters  indicates  the  existence  of  partial  retention 
which  is  not  ready  enough  for  successful  anticipation  but  which 
is  nevertheless  effective.  One  might  anticipate  this  tact  from  the 
nature  of  the  case,  quite  independent  of  the  magnitude  and  the 
probable  error  of  the  difference.  Such  partial  retention  may  be 
due  to  one  of  two  causes,  or  to  both.  (1)  One  part  of  a  syl¬ 
lable  may  be  forgotten  more  rapidly  than  another  part.  (2)  The 
association  link  may  be  so  weakened  that  it  cannot  be  reinstated 
within  the  short  time  limit  of  2  sec.  We  shall  later  see  that  ex- 


THE  CONDITIONS  OF  RETENTION 


25 


tending  the  time  limit  for  recall  increases  the  score  by  a  far 
greater  amount  than  does  the  present  process.  A  time  limit  is 
detrimental  to  partial  retention. 

It  is  important  to  notice  that  by  scoring  the  number  of  letters 
instead  of  syllables,  the  shape  of  the  curve  is  not  materially 
changed.  In  Fig.  Ill,  the  curves  for  the  number  of  syllables  and 
for  the  number  of  letters  may  be  compared  by  direct  inspec¬ 
tion. 

2.  The  Difference  between  Scoring  the  Whole  Series  With  and 
Without  the  First  Syllable . 

This  was  done  on  a  priori  grounds.  Apparently,  there  seems 
to  be  a  difference  between  the  anticipation  of  the  first  syllable  of 
the  series  and  of  the  other  eleven.  For  each  of  the  eleven,  antici¬ 
pation  is  facilitated  by  that  part  of  the  series  which  is  already 
exposed.  The  associative  bond  is  aroused  by  so  many  “cues,” 
such  as  visual,  auditory  and  vocal,  which  are  not  available  for  the 
first  syllable.  Such  is  not  the  case  with  written  reproduction. 
For  there  the  subject  may  begin  from  any  point  of  the  series  and 
run  forwards  and  backwards. 

Specifically  speaking,  the  ground  for  singling  out  the  first 
syllable  of  the  series  is  perhaps  insecure.  Association  is  effective 
not  only  between  immediately  consecutive  syllables,  but  also  in 
the  most  criss-cross  way  imaginable.5  So  even  the  recall  of  the 
first  syllable  will  be  helped  by  the  anticipatory  re-instatement  of 
the  succeeding  members.  But  in  general,  one  may  consider  the 
association  between  two  like  members  of  a  series  as  quantitatively 
different  from  that  between  one  of  these  members  and  another 
dissimilar  factor. 

When  the  first  syllable  was  thus  excluded,  we  obtained  the 
comparative  results  of  Table  IX. 

TABLE  IX 


20  min. 

1  hr. 

2  hrs. 

1  day 

2  days 

For  12  syllables . 

.  67.8 

50.2 

39-0 

17.8 

10.0 

“  11  “  . 

.  64.9 

46.0 

32.0 

130 

8.3 

Quite  beyond  our  expectation,  the  averages  for  12  syllables  ex¬ 
ceed  those  for  1 1  at  every  interval.  The  first  syllable  was  more 

5  Cf.  Ebbinghaus,  Op.  cit.,  Ch.  IX. 


2  6 


C.  W.  LUH 


often  correctly  anticipated  than  the  average  of  the  other  II. 
Thus  the  lack  of  associative  “cues”  seems  to  be  more  than  com¬ 
pensated  by  the  favorable  effect  of  primacy,  and  our  a  priori 
conclusions  become  groundless. 

j.  The  Difference  between  Scoring  and  Not  Scoring  Position 
and  Sequence  in  Written  Reproduction. 

As  already  stated,  written  reproduction  was  scored  ( i )  as  to 
the  gross  amount  of  retention  and  (2)  as  to  that  factor  plus 
position  and  sequence.  In  the  latter  case,  the  gross  amount  was 
scored  and  position  and  sequence  J4  each.  The  comparative 
results  are  presented  in  Table  X. 

TABLE  X 


20  min. 

1  hr. 

4hrs. 

1  day 

2  days 

With  position  and  sequence.... 

...  80.3 

73-1 

50.3 

32.5 

22.6 

Without  position  and  sequence. 

. . .  88.1 

82.1 

60.5 

39-2 

26.7 

Scoring  position  and  sequence  apparently  decreases  the  amount 
of  retention.  <  It  is,  of  course,  much  more  probable  for  a  syllable 
to  be  reproduced  than  to  be  reproduced  in  the  original  position 
and  sequence.  On  the  other  hand,  it  is  also  remarkable  that  there 
are  not  so  many  instances  in  which  a  syllable  is  remembered  as 
to  its  position  and  sequence  but  only  vaguely  in  specific  content. 
The  above  differences  would  certainly  be  more  prominent  if  we 
had  taken  into  account  the  extent  of  chance  in  our  method  of 
scoring. 

Later  we  shall  see  that  the  decrease  in  the  amount  of  retention 
due  to  scoring  position  and  sequence  is  not  limited  to  the  con¬ 
ditions  of  this  series  of  experiments.  The  phenomenon  was  repro¬ 
duced  in  a  second  series  of  experiments  in  which  the  degree  of  the 
original  learning  was  varied.  Still  the  difference  in  amount  is 
not  such  as  to  change  the  general  shape  of  the  curve.  Compare 
Fig.  Ill  for  this  series  of  experiments. 

4.  The  Difference  between  Scoring  Preliminary  and  Final 
Records. 

In  describing  the  methods  of  scoring,  we  mentioned  that  rec¬ 
ords  were  taken  of  the  amount  of  error  in  written  reproduction, 
of  the  amount  of  material  recalled  upon  the  lapse  of  preliminary 


THE  CONDITIONS  OF  RETENTION 


27 


time  limits  in  recognition  and  written  reproduction  and  of  the 
amount  of  time  spent  in  the  whole  process  of  recall  in  recognition, 
reconstruction  and  written  reproduction.  These  results  will  be 
presented  and  compared  in  another  section. 

5.  Corroborative  Data  from  the  Second  Series  of  Experi¬ 
ments. 

In  the  second  series  of  experiments,  the  Reproduction,  Recog¬ 
nition,  and  Reconstruction  methods  of  testing  results  were  used 
when  the  material  was  learned  with  different  degrees  of  mas¬ 
tery.  When  the  degree  of  learning  was  exactly  the  same  as  in 
the  first  series  of  experiments,  the  two  series  of  values  cor- 
roborated  each  other  to  a  remarkable  extent.  The  values  tor 
both  series  of  experiments  are  presented  in  Table  XI.  A  fuller 
description  of  the  conditions  of  the  second  series  is  to  be  found 
at  the  beginning  of  Chapter  III. 


TABLE  XI 


Written  reproduction 

20  min. 

1  hr. 

4  hrs. 

1  day 

2  days 

1st  series  of 

experiments. . . . 

. .  88.1 

82.1 

60.5 

39-2 

26.7 

2d  series  of 

experiments . . . . 

.  .  90.6 

85.8 

64.8 

45-6 

40.2 

Average  . 

Scoring  position  and  sequence 

. .  89.4 

84.0 

62.6 

42.4 

33-5 

1st  series  of 

experiments . . . . 

. .  80.3 

73-1 

50.3 

32.5 

22.6 

2d  series  of 

experiments. . . . 

•  •  86.5 

81.2 

58.0 

37-5 

33-5 

Average  . . 

. .  83.4 

77-2 

54-2 

35-0 

28.1 

Recognition 

1st  series  of 

experiments. . . . 

. .  97.8 

.94.6 

93-3 

74-6 

7i.5 

2d  series  of 

experiments. . . . 

. .  95-8 

95-0 

91.6 

77-6 

78.9 

Average  .  . 

. .  96.8 

94.8 

92.5 

76.1 

75-2 

Reconstruction 

1st  series  of 

experiments. . . . 

..  91.5 

89.7 

75-4 

50.9 

38.6 

2d  series  of 

experiments. . . . 

•  •  89.3 

90.4 

74-9 

48.6 

44-0 

Averages  . 

. .  90.4 

90.1 

75-2 

49-7 

41-3 

For  the  shorter  intervals,  the  validity  of  either  set  of  values 
is  self-evident  and  beyond  question.  But  the  difference  between 
the  two  sets  increases  with  the  length  of  the  interval.  This  fact 
is  to  be  later  considered  as  a  characteristic  of  individual  differ¬ 
ences  in  the  ability  to  recall. 

In  written  reproduction,  when  position  and  sequence  were 
scored,  the  values  of  the  first  series  were  not  so  closely  repro- 


28 


C.  W.  LUH 


duced  in  the  second  series  tor  the  short  intervals  but  more 
closely  reproduced  for  the  long  intervals.  The  validity  of  the 
long  interval  values  is  questionable.  As  to  the  short  intervals, 
we  have  already  stated  that  the  method  of  scoring  position  and 
sequence  is  not  very  reliable. 

Comparison  and  Interpretation  of  data 

From  Fig.  II,  two  general  phenomena  are  easily  observable, 
(i)  The  curve  for  relearning  does  not  fall  as  rapidly  as  the  other 
curves  and  it  intersects  with  the  reconstruction  and  written 
reproduction  curves  as  the  length  of  the  interval  is  increased. 
Were  it  possible  to  fit  each  series  of  empirical  data  to  an  ideal 
curve  or  family  of  curves,  one  would  still  be  confronted  with  the 
difficulty  that  relearning  does  not  satisfy  quite  the  same  type  of 
equation  as  the  other  memory  processes.  By  increasing  the  num¬ 
ber  of  constants,  we  might  represent  all  the  series  of  values  by 
a  general  logarithmic  equation  which  applies  to  all  conditions, 
but  our  ignorance  of  the  actual  and  specific  course  of  forgetting 
would  be  as  profound  as  ever.  Suppose  that  the  values  of  all 
the  constants  are  given  or  calculated,  which  is  a  wild  supposition 
in  the  light  of  our  present  knowledge  of  memory  processes.  We 
could  then  be  sure  of  only  one  thing,  viz.,  Relearning  and  the 
other  processes  do  not  satisfy  the  same  type  of  logarithmic  equa¬ 
tion. 

(2)  With  the  exception  of  the  relearning  curve,  the  other 
curves  are  more  or  less  similar.  The  similarity  becomes  more 
prominent  at  the  end  of  the  4-hr.  interval.  It  may  even  be  said 
that  after  the  lapse  of  that  interval,  the  difference  between  any 
two  memory  processes  except  relearning  and  probably  recogni¬ 
tion,  measured  at  any  time,  is  a  definite  amount  which  is  con¬ 
stant  for  those  two  processes.  Recognition  is  in  many  respects 
similar  to  relearning.  It  favors  the  longer  intervals  and  partial 
retention. 

This  similarity  of  the  curves  is  reproduced  in  the  second  series 
of  experiments,  as  may  be  seen  in  Table  XI. 


THE  CONDITIONS  OF  RETENTION 


29 


(  j)  Comparison  of  the  Relearning  and  the  Other  Curves . 

One  possible  reason  for  the  disparity  as  discussed  under  (1), 
one  might  assume,  may  be  traced  back  to  defects  in  the  methods 
of  measurement,  which  do  not  take  into  enough  consideration 
the  amount  of  partial  retention.  As  we  shall  later  develop,  the 
processes  of  memory  fade  away  gradually,  from  complete  reten¬ 
tion  to  bare  recognition.  One  may  thus  be  led  to  expect  that  the 
amount  of  partial  and  uncertain  retention  increases  in  direct 
proportion  to  the  length  of  the  interval.  Could  we  devise  a  finer 
method  by  which  each  memory  process  is  measured  in  its 
entirety,  the  score  for  each  interval  would  be  increased  by  the 
amount  of  partial  retention.  But  the  increment  would  make  very 
little  difference  in  the  shape  of  the  curve  for  the  shorter  intervals 
when  the  total  amount  of  partial  retention  is  rather  small;  and  in 
fact,  we  see  that  the  fall  of  the  relearning  curve  is  similar  to  the 
others  for  the  short  intervals.  In  other  words,  the  defects  in  the 
methods  of  measurement  could  not  be  so  easily  detected  when  the 
interval  is  short.  For  the  long  intervals,  these  defects  could  be 
remedied  only  by  carefully  scoring  the  amount  of  partial  reten¬ 
tion.  Since  the  latter  is  thought  to  increase  with  the  time  inter¬ 
val,  the  results  thus  scored  would  manifestly  be  a  curve  which 
slopes  down  much  less  abruptly  and  approaches  a  type  like  that 
of  relearning. 

Now  the  argument  as  here  presented  assumes  at  least  two 
things.  A.  A  more  accurate  method  of  measurement  will  bring 
to  light  the  amount  of  partial  retention  so  much  so  that  the  shape 
of  the  curve  will  be  changed.  B.  The  amount  of  partial  retention 
increases  with  the  time  interval. 

As  to  B,  we  suggest  that  this  assumption  is  not  always  true 
and  shall  try  to  demonstrate  the  fact  in  Ch.  IV. 

Assumption  A  seems  more  plausible  only  because  we  cannot 
develop  a  method  of  such  magical  accuracy.  If  the  methods  of 
measurement  were  the  only  faulty  factor,  then  the  improvement 
of  technique  by  way  of  refining  these  methods  would  in  propor¬ 
tion  make  the  other  curves  approach  more  closely  the  relearning 
type  of  curve.  However,  within  the  limits  of  our  investigation, 


30 


C.  W.  LUH 


the  shape  of  the  curves  do  not  materially  change  on  account  of 
minute  variations  in  the  methods  of  measurement.  The  follow¬ 
ing  facts  indicate  that  the  differences  under  consideration  are 
more  fundamental  than  merely  a  matter  of  technique. 

(a)  In  anticipation,  scoring  the  number  of  letters  as  well  as 
syllables  increases  the  value  by  including  partial  retention,  but 
the  increments  are  not  such  as  to  make  the  curve  fall  less  rapidly 
than  does  scoring  the  number  of  syllables  alone  (Fig.  III). 

(b)  In  written  reproduction,  scoring  position  and  sequence  in 
addition  to  the  amount  of  reproduced  material  does  not  change 
the  shape  of  the  curve  very  appreciably.  When  position  and 
sequence  are  not  scored,  more  allowance  is  made  for  partial  re¬ 
tention,  for  a  syllable  which  is  retained  only  as  to  its  content 
and  not  its  relative  order  is  scored  as  much  as  one  which  is 
completely  retained.  According  to  the  proposed  theory,  scoring 
position  and  sequence  would  make  the  curve  fall  much  more 
rapidly.  This  is  not  a  fact. 

(c)  In  recognition  and  written  reproduction,  as  will  be  dis¬ 
cussed  later  on,  extending  the  time  limit  for  recall  so  as  to  make 
more  room  for  the  reinstatement  of  partial  retention  does  not 
change  the  general  shape  of  the  curve,  though  the  increment  of 
the  score  after  the  extension  of  the  time  limit  in  recognition  does 
increase  with  the  length  of  the  interval  so  that  the  curve  slopes 
toward  the  abscissa  more  gradually.  (For  recognition  in  the 
first  series  of  experiments,  see  Fig.  III.) 

Thus,  scoring  partial  anticipation,  neglecting  position  and 
sequence  in  written  reproduction  and,  finally,  extending  the  time 
limit  for  recall  all  fail  to  eliminate  the  apparent  difference  be¬ 
tween  the  relearning  curve  and  the  other  curves.  The  assump¬ 
tions  of  the  theory  cannot  be  substantiated. 

It  is  doubtful  whether  the  relearning  curve  can  be  directly 
compared  with  any  of  the  rest.  Relearning,  being  a  composite 
method,  may  be  analyzed  into  anticipation  and  subsequent  learn¬ 
ing.  Most  probably,  the  subsequent  learning  is  a  function  of  the 
amount  of  anticipation.  The  more  the  amount  of  anticipation, 
the  less  the  number  of  presentations  necessary  for  relearning. 


THE  CONDITIONS  OF  RETENTION 


3i 


If  any  such  causal  connection  be  found  to  be  generally  valid,  then 
the  relearning  values  can  be  constructed  from  the  original  learn¬ 
ing  and  the  amount  of  anticipation.  Only  such  analysis  could 
bring  out  any  natural  relationship  that  may  exist  between  the 


amount  of  retention  and  the  time  necessary  for  relearning.  For 
the  present  these  two  factors  cannot  but  be  treated  as  independent 
values,  particularly  for  the  following  reason. 

The  values  for  relearning  are  based  upon  the  time  of  learning 
and  relearning,  the  proficiency  of  retention  being  measured  by 
a  ratio  of  time;  while  the  values  for  the  other  curves  are  built 
on  an  almost  totally  different  criterion.  With  the  latter,  the 
standard  of  proficiency  is  not  the  length  of  time,  but  the  ability 
to  retain  the  whole  series,  and  different  degrees  of  retention  are 
measured  as  steps  approaching  that  standard. 

For  this  reason,  the  time  for  relearning  cannot  be  interpreted 
in  terms  of  the  amount  of  retention,  but  both  must  be  taken  into 
consideration  in  order  to  understand  the  phenomenon  of  reten¬ 
tion  quantitatively.  A  score  made  by  the  “saving  method’'  can¬ 
not  be  converted  into  another  score  except  as  to  mean  the  amount 
of  time  saved.  As  to  the  measurements  for  the  amount  of  re¬ 
tained  material,  the  same  course  of  reasoning  will  lead  to  the 
conclusion  that  these  measurements  do  not  indicate  anything  as 
to  the  relative  difficulty  experienced  in  mastering  the  material. 
For  instance,  60%  of  retention  is  three  times  as  high  as  20% 
with  respect  only  to  the  actual  amount  of  material;  it  explains 


32 


C.  W.  LUH 


nothing  as  to  how  it  was  acquired,  or  how  much  it  is  really  worth 
as  compared  with  another  amount  acquired  with  the  expenditure 
of  a  larger  or  smaller  amount  of  time. 

Perhaps  a  consideration  of  the  shape  of  the  learning  curves 
for  memory  as  involved  in  the  relearning  method  will  bring 
to  mind  more  distinctly  the  disparity  between  the  two  standards 
of  measurement,  namely,  time  and  amount.  If  in  both  learning 
and  relearning,  the  effect  of  each  presentation  of  the  series  upon 
learning  were  constant,  the  learning  curves  would  then  satisfy 
equations  of  the  first  degree  such  as  hypothetically  represented 
in  Fig.  IV.  Further,  if  the  effect  were  constant  for  relearning 


after  any  time  interval  and  with  any  amount  of  actually  retained 
and  reproduced  material,  then  the  curves  would  be  parallel.  In 
such  a  case,  the  amount  of  retention  would  be  a  function  of  the 
time  necessary  for  relearning,  and  vice  versa.  For,  referring  to 
Fig.  IV,  the  amounts  of  retained  material  after  different  time 
intervals  are  Y0Y3,  Y0Y2,  etc.  Correspondingly,  according  to  the 
“saving  method,”  the  percentages  of  retention  and  forgetting  are 
calculated  according  to  distances  on  the  line  parallel  to  the  ab¬ 
scissa  which  represents  the  number  of  presentations  necessary 
for  learning  or  relearning.  X0Y4  is  the  number  of  presentations 
in  learning.  X3Y4  is  the  number  of  presentations  necessary 
for  relearning  after  the  lapse  of  an  interval  when  the  amount  of 
retained  material  as  represented  on  the  ordinate,  is  Y0Y3.  The 
percentage  of  forgetting  for  that  interval  is  X3  Y4  /  X0  Y4.  It 
corresponds  to  the  amount  Y3  Y4.  Similarly,  X2  Y4  /  X0  Y4  cor¬ 
responds  to  Y2  Y4,  Xi  Y4  /  X0  Y4  corresponds  to  Y4  Y4,  etc.  It 


THE  CONDITIONS  OF  RETENTION 


33 


is  clear  that  since  the  learning  curves  are  supposed  to  be  parallel, 
the  percentages  of  forgetting,  or  of  retention,  thus  calculated 
from  the  abscissa  would  always  be  proportional  to  the  percentages 
calculated  from  the  ordinate.  Then  the  curves  of  retention  based 
upon  the  “saving  method and  upon  the  amount  of  recalled 
material  would  be  similar ,  when  plotted  on  the  same  scale. 

As  a  matter  of  fact,  the  learning  curves  for  memory  are  not 
parallel  straight  lines.  Practically  all  the  curves  so  far  deter¬ 
mined  are  negatively  accelerative,  including  especially  the  recent 
work  of  Kjerstad.6  This  is  also  corroborated  by  our  own  re¬ 
sults  in  both  learning  and  relearning.  The  degree  of  negative 
acceleration  in  the  relearning  process  also  varies  with  the  time  in¬ 
terval  or  the  amount  of  actually  retained  material.  That  is,  if 
the  curves  follow  the  same  law  of  negative  acceleration,  they  can 
then  be  represented  as  in  Fig.  V.  In  the  figure,  Y3  Y4,  Y2  Y4,  etc. 
represent  respectively  the  amounts  of  forgetting  after  different 
time  intervals,  X3  Y4,  X2  Y4,  etc.  represent  respectively  the  cor¬ 
responding  number  of  presentations  necessary  for  relearning  for 
each  of  the  assigned  time  intervals.  From  that  figure,  two  facts 
become  self-evident. 

a)  Not  only  do  X  and  Y  differ  in  the  scale  and  unit  of  measure¬ 
ment,  but  the  functional  relationship  between  the  two  is  not  so 
simple  as  that  represented  in  Fig.  IV  and  not  such  as  could  be 
easily  determined.  Referring  back  to  Fig.  II,  this  difference  in 
the  units  of  the  scales  and  this  complex  and  unknown  functional 
relationship  between  them  would  mean  that  the  absolute  height 
of  the  retention  curve  for  relearning,  as  compared  with  that  of 
the  other  retention  curves,  cannot  be  interpreted  by  mere  inspec¬ 
tion.  The  absolute  values  of  the  curves  cannot  be  directly  com¬ 
pared. 

b)  But  the  more  significant  fact  is  that  these  very  character¬ 
istics  of  the  learning  curves  will  directly  lead  to  the  particular 
difference  between  the  shape  of  the  relearning  curve  for  retention 
and  of  the  other  retention  curves,  as  seen  in  Fig.  II.  In  Fig.  V, 
the  number  of  presentations,  X3Y4,  X2  Y4,  etc.  increases  at  first 
more  rapidly  than  the  corresponding  amounts  of  forgetting, 

6  Op.  cit. 


34 


C.  W.  LUH 


Y3  Y4,  Y2  Y3,  etc. ;  but  less  rapidly  when  the  amount  of  actually 
retained  material  is  small,  i.  c.,  when  the  time  interval  is  increased. 
Now  if  we  plot  the  values  on  the  ordinate  against  the  variable 
of  time  in  such  manner  as  manifested  by  the  retention  curves 


r,3  x. 


for  the  amount  of  reproduced  material  (A),  and  if  we  further 
draw  a  curve  (B)  for  the  retention  values  as  determined  from  the 
abscissa  on  the  basis  of  (A),  their  relationship  will  be  such  as 
given  in  Fig.  VI.  The  difference  between  the  two  is  exactly  what 
we  observed  in  Fig.  II. 

Thus,  the  difference  between  the  relearning  curve  for  reten¬ 
tion  and  the  other  retention  curves  is  not  due  to  the  phenomenon 
of  retention  as  such,  but  to  the  characteristic  of  the  learning 
curve.  If  the  latter  were  invariably  a  simple  logarithmic  curve,  it 
would  necessarily  follow  that  the  forgetting  curve  as  determined 
by  the  “saving  method”  would  be  logarithmic.  When  this  rela¬ 
tionship  obtains,  as  claimed  by  most  of  our  predecessors,  it  is 
important  to  remember  that, 

a.  The  curve  of  forgetting  for  the  saving  method  is  logarith¬ 
mic  only  because  it  involves  the  ratio  of  two  logarithmic  learning 


curves. 


b.  Similar  phenomena  cannot  be  expected  to  reappear  when  the 
same  factors  are  not  involved. 

The  Unsatisfactoriness  of  the  Relearning  Method. 

It  is  now  evident  that  neither  time  nor  amount  is  a  complete 
measurement  for  retention,  but  both  are  not  equally  convenient. 
A.  The  first  unsatisfactoriness  of  the  relearning  method  is  that 


THE  CONDITIONS  OF  RETENTION 


35 


it  achieves  much  less  validity  of  data  for  the  same  expenditure 
of  time  as  compared  with  the  other  methods. 

As  a  test  for  validity,  we  use  the  mean  deviation  of  the  values 
of  all  the  series  which  a  subject  learns  or  reproduces  for  each 
specific  interval.  This  M.  D.  may  be  made  directly  comparable 

100M.  D. 

with  other  M.  D.’s  by  applying  Pearson’s  formula  V  — - : - . 

Median 

The  greater  the  coefficient  V,  the  less  is  the  validity.  Five  of 
the  subjects  learned  five  series  for  each  of  the  five  intervals  in 
the  first  series  of  experiments.  Five  is  a  ridiculously  small  num¬ 
ber  for  such  statistical  treatment.  If,  however,  all  the  results 
point  uniformly  in  one  direction,  most  probably  there  is  an  actual 
difference  in  the  degree  of  validity  of  these  values.  Table  XII 
presents  the  results  for  only  two  intervals,  20  min.  and  1  hr. 
Beyond  that,  the  variability  of  the  relearning  method  becomes  so 
large  as  to  make  such  comparison  superfluous  and  meaningless. 
A  ?  mark  indicates  that,  of  the  two  intervals  and  the  two  par¬ 
ticular  methods  compared,  the  coefficient  of  variability  is  larger 
for  one  method  at  one  interval,  and  for  the  other  at  the  other. 
In  a  similar  way,  a  +  sign  means  larger  variability  for  relearn¬ 
ing  at  both  intervals. 


SUBJECT 

TABLE  XII 

ANTICIPATION  RECOGNITION 

RECONSTRUCTION 

W.  REP. 

D 

? 

+ 

+ 

? 

Le 

? 

+ 

? 

+ 

Lo 

? 

+ 

+ 

p 

R 

+ 

? 

? 

p 

W 

? 

+ 

+ 

+ 

Of  all  the  paired  comparisons,  none 

is  distinctly  in 

favor  of 

the  relearning  method. 

Its  coefficient 

of  variability 

is  higher 

than  that  of  any  other  method.  That  is,  for  equal  expenditure  of 
time  and  energy,  relearning  produces  less  satisfactory  results  than 
does  any  other  method. 

B.  In  addition  to  the  above,  the  relearning  method  makes  im¬ 
possible  certain  correlation  studies  which  are  easily  accessible  to 
the  other  methods.  Questions  like  the  following  have  to  be 
answered  one  way  or  another,  (a)  What  is  the  relation  between 


36 


C.  W.  LUH 


the  speed  of  learning  and  the  amount  of  retention  for  each  inter¬ 
val?  (b)  For  all  the  series  learned  by  the  same  subject,  what  is 
the  relation  between  the  difficulty  of  learning  and  the  amount 
of  retention,  etc.?  As  to  question  (a),  the  problem  of  the  cor¬ 
relation  between  “immediate”  and  “permanent”  memory  has 
claimed  a  goodly  number  of  working  days.  Very  little  has  been 
written  on  question  (b),  but  Ebert  and  Meumann7  once  raised  the 
problem  whether  subject  matter  that  is  readily  learned  is  forgot¬ 
ten  more  rapidly  or  more  slowly  than  that  which  requires  greater 
labor  in  memorizing.  In  dealing  with  these  problems,  the  re¬ 
learning  method  was  generally  used.  Relearning,  as.  we  already 
discussed,  involves  two  learning  processes.  Suppose  a  number  of 
syllable  series  to  be  learned  in  X,  X',  X",  .  .  .  presentations 
and  relearned  in  Y,  Y',  Y ",  .  .  .  presentations.  The  amounts 

Y  Y'  Y" 

of  forgetting  will  be  - ,  - ,  - ,  .  .  .  Learning  and 

X  X'  X" 

forgetting  involve  the  same  factor  X,  X',  X",  .  .  .  That  fact 
deprives  any  correlation  study  of  its  real  significance.  If  it  is 
further  argued  that  the  percentage  of  retention  is  determined  by 
X — Y,  X' — Y',  X" — Y",  ....  which  are  independent  values, 
we  suggest  that  these  values  can  be  more  reasonably  established 
by  some  other  methods  which  directly  measures  the  amount  of 
reproduced  material. 

(2)  Comparison  of  the  Curves  which  Represent  Only  the 
Amount  of  Reproduced  Material. 

We  have  explained  why  the  relearning  and  the  other  curves  are 
different  in  general  form,  and  now  proceed  to  the  problem  why 
these  other  curves  differ  in  absolute  numerical  value.  But  we 
cannot  treat  the  problem  without  first  proving  that  the  numerical 
differences  are  real  and  not  adventitious. 

First,  we  can  refer  back  to  the  data  for  each  individual  sub¬ 
ject,  which  constitute  the  group  averages.  From  the  group 
curves,  recognition  has  a  higher  value  than  reconstruction  for 
each  of  the  five  intervals.  The  same  relation  holds  for  recon¬ 
struction  and  written  reproduction,  and  for  the  latter  and  antici- 

7  “Ueber  einige  Grundfragen  der  Psychologie  der  Uebungsphenomene  im 
Bereiche  des  Gedachtnisses,”  Archive  f.  Gesamte  Psy.,  Vol.  IV,  1904,  pp.  193-4. 


THE  CONDITIONS  OF  RETENTION 


37 


pation.  This  particular  order  of  proficiency  for  the  several 
measurements  of  retention  holds  true  for  the  majority  of  the 
subjects.  Thus,  of  the  20  individual  values,  10  from  each  series 
of  experiments,  which  constitute  the  final  recognition  score  for 
the  20  m:n.  interval,  only  one  is  higher  than  its  corresponding 
value  which  goes  to  make  the  final  score  for  reconstruction  for 
the  same  interval,  etc.  Table  XIII  presents  these  facts  in  brief. 


TABLE  XIII 

Percentage  of  Individual  Cases  which  Correspond  to 

Group  Results 


20  min. 

1  hr. 

4  hrs. 

1  day 

2  days 

Anticipation  cf.  written  reproduction* 

100 

100 

87 

87 

75 

Written  reproduction  cf.  reconstruction 

.  60 

75 

75 

70 

65 

Reconstruction  cf.  recognition  . 

95 

80 

95 

95 

95 

*  Only  8  values  from  8  subjects  in  the  1st  series  of  experiments.  The  rest 
are  constituted  of  20  values  from  20  subjects  in  both  series  of  experiments. 


Secondly,  the  validity  of  the  numerical  differences  may  be 
proved  by  the  magnitude  of  their  probable  errors,  as  presented  in 
Table  XIV. 


TABLE  XIV 


Difference  between 

20  min. 

I  hr. 

4  hrs. 

1  day 

2  days 

Antic,  and  Wr.  Rep . 

20.3 

31.9 

21-5 

21.4 

16.7 

P.  E.  of  difference . 

Difference  between 

4-5 

3-7 

5-5 

7.0 

6.1 

Wr.  Rep.  and  Reconstruction... 

1.0 

6.1 

12.6 

7-3 

7.8 

P.  E.  of  difference  . 

Difference  between 

1. 1 

1-7 

2.7 

4-5 

4.3 

Recons,  and  Recognition . 

6.4 

4-7 

17.3 

26.4 

33-9 

P.  E.  of  difference . 

1.5 

1.9 

2.2 

4-3 

4-3 

The  P.  E.  of  the  difference  between  reconstruction  and  written 
reproduction  can  be  reduced  by  increasing  the  number  of  subjects. 
In  other  words,  the  values  for  reconstruction  and  written  repro¬ 
duction  may  be  slightly  changed  with  the  increase  in  the  number 
of  subjects,  especially  for  the  20  min.  interval.  That  there 
is  a  positive  difference  in  favor  of  reconstruction  at  each  of  the 
intervals  is  unmistakable.  The  validity  of  all  the  other  differences 
is  self-evident. 

Returning  now  to  the  group  curves,  we  further  find  that,  while 


38 


C.  IV.  LUH 


after  the  lapse  of  the  4  hr.  interval  the  course  of  the  curves  be¬ 
come  more  or  less  parallel,  such  is  not  the  case  for  the  shorter 
intervals.  There  the  decreases  in  value  are  more  abrupt  for  cer¬ 
tain  curves  than  for  others.  On  the  whole,  the  one  that  begins 
the  lowest  at  20  min.  falls  the  most  rapidly  so  that  the  curves 
become  farther  and  farther  apart  as  the  length  of  the  interval 
increases.  So  the  Ebbinghaus  tradition  is  substantiated  by  our 
data  to  that  extent. 

However,  the  negative  acceleration  theory  of  the  curve  of  for¬ 
getting  does  not  hold  for  all  of  our  values.  The  two  notable 
exceptions,  as  may  be  seen  from  pp.  21-22  are: 

1.  In  recognition,  the  transition  from  1  hr.  to  4  hrs.  is  much 
less  accelerative  than  that  between  4  hrs  and  1  day. 

2.  In  written  reproduction,  the  curve  approaches  a  straight 
line  between  20  min.  and  4  hrs. 

A  significant  fact  is  that  these  exceptions  in  the  first  series  of 
experiments  were  reproduced  in  the  second  series.  Further,  im¬ 
posing  a  time  limit  upon  the  act  of  recognition  and  scoring  posi¬ 
tion  and  sequence  in  written  reproduction  did  not  in  the  least 
ameliorate  these  peculiarities.  Is  the  curve  of  forgetting  a  loga¬ 
rithmic  curve,  as  has  been  repeatedly  maintained?  These  facts 
must  be  taken  into  consideration  and  explained. 

One  must  also  remember  the  course  of  the  curves  after  the 
lapse  of  the  4-hr.  interval,  as  described  in  a  preceding  paragraph. 
What  is  its  bearing  on  a  general  logarithmic  equation  ? 

From  the  above,  we  may  still  conclude  that,  of  two  memory 
processes,  the  one  that  commands  a  higher  “initial”  amount  of 
forgetting  tends  to  fade  away  more  rapidly  than  the  other.  This 
acceleration  approaches  a  limit  at  the  end  of  4  hrs.,  and  does  not 
resume  its  initial  course  even  to  the  end  of  2  days. 

One  word  as  to  what  is  meant  by  an  “initial”  amount  of  for¬ 
getting,  a  term  first  used  by  Bean.  When  retention  is  measured 
at  the  end  of  20  min.,  we  see  only  a  cross-section  of  the  stream  of 
forgetting,  to  use  James’  old  metaphor.  From  our  data  we  can¬ 
not  determine  whether  the  grade  of  the  headwaters  is  steep  or 
level,  or  where  the  grade  actually  begins.  In  other  words,  we  do 


THE  CONDITIONS  OF  RETENTION 


39 


not  know  what  the  “initial”  amount  of  forgetting  is,  for  each 
process.  The  quantitative  differences  as  we  measure  at  the  end 
of  20  min.  may  doubtless  be  traced  back  to  differences  of  the 
same  kind.  We  assume  that,  if  at  20  min.,  retention  as  measured 
by  the  anticipation  method  is  less  than  by  the  recognition  method, 
this  was  also  true  for  shorter  periods  than  20  min.,  though  not  in 
the  same  ratio  and  by  the  same  amount.  But  in  fact,  forgetting 
for  one  process  may  not  begin  at  the  same  point  as  for  another. 

This  is  particularly  true  for  written  reproduction,  recognition 
and  reconstruction.  When  the  method  of  presentation  in  the 
original  learning  is  different  from  the  method  of  testing,  we  can 
no  longer  compare  directly  the  amount  of  immediate  retention 
with  the  values  that  determine  the  curves  of  forgetting.  In  anti¬ 
cipation  and  relearning  we  know  that  the  amount  of  retention 
immediately  after  learning  is  100%  so  that  we  can  trace  these 
curves  back  to  Y0,  i.  e.,  where  the  length  of  the  interval  is  o. 
But  in  the  other  three  methods,  the  forgetting  curves  begin  at 
20  min.  and  we  cannot  go  back  any  further.  It  is  perhaps  un¬ 
fortunate  that  we  did  not  vary  the  methods  of  the  original  learn¬ 
ing  as  well  as  the  methods  of  testing,  but  then  we  would  have 
introduced  another  constant  and  would  have  made  our  data 
more  difficult  to  interpret. 

Very  likely,  the  quantitative  differences  between  any  two  pro¬ 
cesses  measured  at  any  time  may  be  greatly  reduced  by  trans¬ 
posing  the  curves  so  that  the  points  of  “initial”  forgetting  coin¬ 
cide.  All  this  may  be  empirically  determined.  Unless  such 
problems  are  solved,  the  term  “initial”  forgetting  will  remain 
as  meaningless  as  the  “logarithmic”  curve  of  forgetting. 

Possible  Explanations  for  the  Quantitative  Differences. 

The  conditions  are  complicated.  Perhaps  no  single  explana¬ 
tion  is  sufficient,  but  the  following  are  more  than  likely. 

1)  The  temporal  order  in  which  the  methods  were  applied. 
In  one  half  of  the  series  given  to  each  subject,  anticipation  was 
tested  before  relearning.  In  the  other  half,  written  reproduction 
was  the  first  test  applied.  Recognition  followed  after  written 
reproduction,  and  reconstruction  after  recognition.  The  high 


40 


C.  IV.  LUH 


retention  values  for  recognition  and  reconstruction  and  the  low 
values  for  anticipation  and  written  reproduction  may  partly  be 
due  to  the  presence  or  absence  of  a  preceding  recalling  process. 
For  the  present,  we  cannot  determine  whether  that  effect  actually 
exists  and  to  what  extent.  It  is  probable,  however,  that  the 
effect  of  a  preceding  recalling  process  may  simply  reduce  the 
duration  of  the  succeeding  recalling  process  without  changing 
the  amount  of  recall  of  the  latter.  In  Ch.  VI  we  shall  see  that 
the  average  duration  of  the  written  reproduction  process  was 
longer  than  for  recognition,  and  the  latter  longer  than  for  re¬ 
construction.  It  is  possible,  of  course,  that  a  preceding  recall¬ 
ing  process  affects  both  the  amount  and  the  duration  of  a  suc¬ 
ceeding  one. 

Apparently,  the  explanation  does  not  cover  all  the  facts.  Re¬ 
construction  followed  after  recognition  but  gave  much  the 
smaller  values. 

2)  The  duration  of  the  several  processes.  The  duration  of 
the  anticipation  process  was  24  sec. ;  that  of  written  reproduc¬ 
tion,  5  min.;  while  recognition  and  reconstruction  did  not  have 
time  limits.  So  the  order  of  the  numerical  values  corresponds 
to  the  order  of  the  duration  of  the  processes.  But  as  we  shall 
later  discuss  in  full,  it  took  the  average  subject  much  less  than 
5  min.  to  complete  the  written  reproduction  process.  The  actual 
duration  of  recognition  was  not  half  as  long  as  written  repro¬ 
duction,  and  that  of  reconstruction  was  still  shorter.  The  actual 
differences  in  duration  are  not  proportional  to  the  numerical 
differences  in  the  retention  values.  Written  reproduction  had 
the  longest  duration  but  gave  the  lowest  retention  values  except 
anticipation. 

3)  Differences  in  the  units  of  measurement.  In  anticipation  and 
written  reproduction,  the  scores  were  based  upon  the  amount  of 
reproduced  material.  The  requirement  of  the  recognition  method 
was  merely  that  the  different  members  be  re-instated  upon  the 
presentation  of  the  original  series.  In  reconstruction,  only  po¬ 
sition  and  sequence  were  required.  The  implication  would  be 
that  the  numerical  differences  under  discussion  cannot  be  taken 
too  seriously. 


THE  CONDITIONS  OF  RETENTION 


4i 


However,  this  kind  of  explanation  is,  in  a  way,  begging  the 
question.  In  written  reproduction,  recognition  and  reconstruc¬ 
tion,  we  scored  the  same  records  for  different  values.  Were  the 
scales  and  units  identical,  we  could  not  have  had  more  than  one 
value.  The  required  explanation  is  this :  Given  different  methods 
of  scoring  the  same  records,  why  do  the  results  differ  in  such  a 
characteristic  way?  The  proposed  explanation  only  tells  us  that 
we  should  not  have  used  those  methods.  So  we  are  led  to  the 
fourth  probable  explanation  which  seems  to  us  to  be  most  rea¬ 
sonable. 

4)  The  conditions  of  recall.  The  experimental  situations  un¬ 
der  which  the  subject  was  required  to  recall  were  vastly  different. 
Our  measurements  took  into  consideration,  among  other  things, 

a)  The  retention  of  the  separate  parts  of  a  serial  act  of 

memory  as  called  for  by 

(a)  Written  reproduction,  and 

(b)  Recognition. 

b)  The  associative  links  that  connect  and  combine  these 

parts. 

c)  The  readiness  with  which  they  are  recalled,  as  measured 

by 

(a)  The  amount  of  time  necessary  for  recall  and 

(b)  The  amount  of  material  recalled  within  a  given 

time  limit. 

These  factors  are  not  equally  important  in  all  the  methods  of 
measurement.  The  number  of  these  factors  involved  and  the 
extent  to  which  they  are  involved  determine  the  quantitative  dif¬ 
ferences.  Thus,  by  order  of  the  difficulty  of  recall,  (Figs.  II  and 

III),  the  four  methods  are  ranked: 

1.  Anticipation. 

2.  Written  reproduction,  scoring  position  and  sequence. 

2a  Written  reproduction,  not  scoring  position  and  sequence. 

3.  Reconstruction. 

4.  Recognition,  with  time  limit. 

4a  Recognition,  without  time  limit. 


42 


C.  W.  LUH 


Analyzing  the  number  of  factors  involved,  they  follow : 

1.  Anticipation.  Factors  a)  and  c)  are  both  important,  b) 

is  necessary  for  complete  re-instatement,  but  once  a 
mistake  is  made,  it  is  automatically  corrected  by  the 
exposure  of  the  syllable. 

2.  Written  reproduction,  scoring  position  and  sequence. 

Factors  a)  and  b)  are  equally  important,  c)  is  in¬ 
volved  only  to  the  extent  of  being  able  to  reproduce 
the  material  within  5  min. 

2a  Written  reproduction,  not  scoring  position  and  sequence. 
The  conditions  are  the  same  as  in  2,  minus  b). 

3.  Reconstruction.  Only  b)  is  involved,  being  the  comple¬ 

mentary  of  2a. 

4.  Recognition,  with  the  time  limit,  a)  is  only  slightly  in¬ 
volved,  b)  not  at  all  and  c)  only  to  the  extent  of  being  able  to 
select  the  12  syllables  within  90  sec. 

4a  Recognition,  without  time  limit.  Only  a)  is  partly  in¬ 
volved. 

From  this  we  conclude  that 

1.  The  quantity  of  recall  depends  upon  the  number  of  restrict¬ 
ing  factors  in  the  recall  situation.  The  greater  number  of  such 
factors  and  the  more  exactingly  they  operate,  the  less  the  amount 
of  recall. 

2.  The  proportionality  between  the  number  of  such  factors  and 
the  amount  of  recall  is  an  index  to  the  practical  validity  of  our 
methods  of  measurement.  The  scores  given  by  these  methods  are 
directly  comparable. 

It  is,  therefore,  meaningless  to  say  that  forgetting  in  general 
follows  a  certain  equation.  There  can  be  as  many  curves  of  for¬ 
getting  as  there  are  situations  and  methods  of  measurement. 
We  know  almost  nothing  as  to  the  “initial”  amount  of  forgetting 
and  very  little  as  to  the  general  shape  of  any  curve.  It  may  be 
harmless  to  say  that  forgetting  is  a  logarithmic  function  of  time, 
so  long  as  we  remember  that  the  significant  thing  that  should 
influence  future  investigations  is  not  the  logarithm,  but  the  de¬ 
termination  of  the  constants.  The  latter  we  cannot  deduce  from 
generalizations,  but  can  only  measure  under  variable  conditions. 


III.  RETENTION  AS  A  FUNCTION  OF  THE 
DEGREE  OF  LEARNING 


In  the  second  series  of  experiments,  the  condition  that  was 
varied  was  the  degree  of  the  original  learning.  The  ten  subjects 
of  the  second  group  served  throughout  these  experiments,  each 
learning  at  least  44  syllable  series,  besides  preliminary  practice 
trials.  The  series  and  the  degrees  of  learning  were  distributed 
according  to  the  following  scheme. 

1.  Altogether  we  used  four  degrees  of  learning. 

A.  100%  learning,  with  the  same  conditions  as  in  the  first 

series  of  experiments. 

B.  150%  learning,  in  which  the  subject  was  given  one 

half  of  the  number  of  presentations  in  addition  to 
what  was  required  for  the  first  errorless  anticipation 
of  a  series.  Thus,  if  a  series  was  learned  in  10  pres¬ 
entations,  5  more  were  given.  If  9,  also  5. 

C.  67%  learning.  The  average  number  of  presentations 

was  calculated  for  each  subject  after  he  had  learned 
20  series  besides  the  preliminary  trials.  In  67% 
learning,  he  was  given  two-thirds  of  that  number  of 
presentations.  (The  average  number  was  previously 
taken  to  be  the  total  number  minus  one,  i.e.,  the  num¬ 
ber  of  presentations  in  which  there  was  actual  antici¬ 
pation.  In  the  present  case,  the  total  number  was 
used.) 

D.  33%  learning.  By  the  same  process  of  computation, 

one-third  of  the  total  number  of  presentations  was 
given. 

2.  In  100%,  67%  and  33%  learning,  the  intervals  used  were 
the  same  five  as  in  the  first  series  of  experiments.  Two  of  these 
were  omitted  for  150%  learning,  but  four  others  were  added.  So 
there  were  seven  intervals  for  150%  learning,  viz.,  2  hrs.,  3  hrs., 
4  hrs.,  6  hrs.,  12  hrs.,  1  day  and  2  days.  The  2-hr.  and  3-hr. 
intervals  were  arbitrarily  chosen  after  they  had  been  tried  out 


43 


44 


C.  W.  LUH 


on  several  subjects.  The  object  was  to  select  such  intervals  as 
would  facilitate  the  comparison  of  the  retention  curves  for  150% 
learning  with  the  other  curves  from  the  same  series  of  experi¬ 
ments. 

Two  series  were  given  each  subject  for  each  interval  and  each 
degree  of  learning.  All  the  series  for  100%  and  150%  learning 
except  the  2-hr.  and  3-hr.  ones  were  completed  by  each  subject 
before  he  tried  67%  or  33%  learning.  The  average  number  of 
presentations  for  learning  these  20  series  furnished  the  required 
basis  of  computation  for  determining  67%  and  33%  learning. 
The  2-hr.  and  3-hr.  intervals  for  150%  learning  were  added  at 
the  end  of  the  whole  series  of  experiments  in  order  to  trace  the 
curves  of  forgetting  further  back  toward  the  ordinate.  One 
extra  6-hr.  series  was  given  each  subject  also  toward  the  end  of 
the  experiments  in  order  to  counteract  the  effect  of  diurnal 
variations. 

For  each  degree  of  learning,  care  was  taken  to  distribute  the 
long  and  short  intervals  evenly. 

Only  the  written  reproduction,  recognition  and  reconstruction 
methods  of  measurement  were  used  in  recall. 

Quantitative  Data 

The  results  of  the  experiments  are  tabulated  in  Table  XV  and 
graphically  presented  in  Figs.  VII-IX. 

TABLE  XV 

20  min.  1  hr.  2  hrs.  3  hrs.  4hrs.  6hrs.  12  hrs.  id.  2d. 


Wr.  Rep. 

150%  learning. .  88.0  84.4  81.9  65.6  54.4  38.5  30.8 

100%  .  90.6  85.8  64.8  45.6  40.2 

67%  .  85.4  72.5  65.8  41.5  24.8 

33%  .  67.7  54.0  42.7  26.2  13.7 

Recognition 

150%  .  97-5  95-8  93-3  91-6  92.5  83.2  72.8 

100%  .  95.8  95.0  91.6  77.6  78.9 

67%  .  93-2  93-3  84.7  73.7  61.5 

33%  .  73-3  64.4  546  45.7  25.5 

Reconstruction 

150%  .  87.5  92.1  90.8  78.9  81.3  43.4  43.9 

100%  .  89.3  90.4  74.9  48.6  44.0 

67%  .  92.0  77.9  65.3  56.6  31.8 

33%  .  75-6  61.9  48.1  26.0  20.0 


THE  CONDITIONS  OF  RETENTION 


45 


i.  The  Range  of  Differences. 

As  may  be  seen  from  Table  XV,  recognition,  as  a  rule,  gives 
the  highest  value  for  each  interval  and  for  each  degree  of  learn¬ 
ing.  Reconstruction  generally  occupies  the  second  place  and 
written  reproduction  the  last.  Now  if  we  take  the  difference  be¬ 
tween  the  highest  and  the  lowest  values  for  each  interval  and 
for  each  degree  of  learning,  we  can  make  a  comparative  study 
of  the  range  of  the  differences.  The  facts  are  presented  in  Table 
XVI. 


TABLE  XVI 
Range  of  Differences 


20  min. 

8  hrs. 

4  hrs. 

1  day 

2  days 

33%  . 

.  7-9 

10.4 

1 1.9 

19.5 

12.8* 

67% . 

.  7-8 

20.8 

19.4 

17.1* 

36.7 

100%  . 

.  6.5* 

9.2* 

26.8 

28.0 

387 

150%  . 

1 1.4* 

447 

42.0 

In  this  table  the  highest  value  for  each  interval  is  underlined 
and  the  lowest  marked  with  an  asterisk.  The  tendency  is  for 
the  highest  value,  i.  e.,  the  greatest  range,  to  occur  at  the  shorter 
intervals  for  the  lower  degrees  of  learning  and  at  the  longer 
intervals  for  the  higher  degrees  of  learning.  The  tendency  for 
the  occurence  of  the  smallest  range  is  vice  versa.  These  facts 
reflect  the  characteristic  way  in  which  the  different  retention 
curves  approach  the  x — axis  with  the  increase  in  the  length  of 
the  time  interval. 

In  general,  the  above  range  of  the  differences  increases  with 
the  time  interval,  but  at  different  rates  for  different  degrees  of 
learning.  Theoretically,  a  higher  degree  of  the  original  learn¬ 
ing,  of  course,  increases  the  amount  of  retention  for  all  the 
methods  of  measurement.  But  it  particularly  favors  the  more 
difficult  methods  for  the  shorter  intervals  so  that  the  range  of  the 
differences  between  the  easiest  and  the  most  difficult  methods  is 
small.  As  the  time  interval  is  lengthened,  this  advantage  rapidly 
disappears.  So  the  different  curves  fall  gradually  apart,  and  the 
range  of  the  differences  increases  accordingly. 


4 6 


C.  W.  LUH 


With  a  lower  degree  of  learning,  the  effect  is  generally  to  de¬ 
crease  the  amount  of  retention  for  all  the  intervals  and  all  the 
methods  of  measurement,  but  the  special  advantage  is  on  the 
side  of  the  easier,  not  the  more  difficult,  methods.  This  effect 
increases  the  range  of  the  differences  for  the  shorter  intervals, 
or  at  least  keeps  it  as  large  as  for  the  higher  degrees  of  learning, 
which  means  that  the  range  will  be  proportionally  greater.  An¬ 
other  characteristic  result  of  a  lower  degree  of  learning  is  that, 
while  the  curves  for  all  the  methods  of  measurement  begin  rather 
low,  they  fall  very  slowly  and  keep  almost  parallel  to  each  other. 
The  range  of  the  differences  is  thus  kept  within  a  small  varia¬ 
tion.  For  the  higher  degrees  of  learning,  the  curves  fall  at  such 
different  rates  that  they  grow  farther  and  farther  apart. 

We  have,  therefore,  at  least  three  types  of  curves  resulting 
from  varying  the  degree  of  the  original  learning  and  at  the  same 
time  using  three  methods  of  measurement.  Type  I  begins  high 
and  falls  slowly.  Type  2  begins  high  and  falls  rapidly.  Type  3 
begins  low  and  falls  slowly.  In  order  to  establish  a  general  for¬ 
mula  for  all  these  types,  the  numerical  differences  must  be  more 
accurately  determined. 

2.  Increase  in  the  Degree  of  Learning  and  Diminished  Returns 
in  the  Amount  of  Retention. 

In  Figs.  VII-IX  one  can  easily  observe  that  the  difference  be¬ 
tween  the  curves  for  33%  and  67%  learning  is  the  greatest,  that 
between  the  curves  for  67%  and  100%  learning  very  much  less, 
and  that  between  the  curves  for  100%  and  150%  learning  the 
least  of  all.  The  curves  for  100%  and  150%  learning  often  cross 
each  other  so  that  it  is  sometimes  difficult  to  tell  whether  an  in¬ 
crease  of  50%  of  learning  actually  resulted  in  any  increase  in  the 
amount  of  retention.  In  written  reproduction  they  cross  for 
the  first  time  at  a  point  whose  abscissa  represents  an  8-hr.  inter¬ 
val.  Previous  to  that  point  the  difference  between  the  curves  is 
distinct.  There  is  a  more  decided  difference  between  the  100% 
and  150%  curves  for  recognition  and  reconstruction.  Table 
XVII  presents  the  difference  for  all  three  methods  of  measure¬ 
ment  and  for  all  the  intervals.  The  probable  errors  of  the  differ- 


*057 


THE  CONDITIONS  OF  RETENTION 


47 


48 


C.  W.  LUH 


ences  are  not  included.  They  are  very  high  for  the  smaller  dif¬ 
ferences.  The  larger  differences  are  self-evident. 


TABLE  XVII 


20  min. 

1  hr. 

4  hrs. 

1  day 

2  days 

Written  Reproduction 

Difference 

33  and  67%.... 

17.7 

18.5 

23.1 

15-3 

11. 1 

67  and  100% .... 

5*2 

1 33 

— 1.0 

4.1 

154 

100  and  150%. . . . 

17.1 

—7.1 

— 94 

Recognition 

Difference 

33  and  67%. . . . 

19.9 

28.9 

30.1 

28.0 

36.0 

67  and  100% .... 

2.6 

1.7 

6.9 

3-9 

174 

100  and  150%. . . . 

1-7 

5-6 

— 6.1 

Reconstruction 

Difference 

33  and  67%.... 

16.4 

16.0 

17.2 

30.6 

11.8 

67  and  100% .... 

—2.7 

12.5 

9.6 

— 8.0 

12.2 

100  and  150%. . . . 

15.9 

—5.2 

— O.I 

—  sign  indicates  that,  of  the  two  values  compared,  the  one  for  the  higher 
degree  of  learning  is  numerically  smaller. 


At  the  outset,  one  might  assume  that  this  phenomenon  of 
diminished  returns  could  be  due  either  to  (i)  practice  effect  or 
to  (2)  difficulties  in  the  original  learning. 

(1)  As  the  series  of  experiments  occupied  more  than  three 
months,  the  proficiency  of  learning  for  most  of  the  subjects  was 
somewhat  improved.  The  extent  of  this  improvement  we  shall 
develop  in  another  section.  After  five  weeks  of  practice  in  100% 
and  150%  learning,  there  is  no  wonder  that  they  could  now  use 
the  67%  of  the  average  number  of  presentations  to  greater  ad¬ 
vantage.  The  average  number  was  calculated  from  the  learn¬ 
ing  of  the  first  20  series  when  the  practice  effect  was  still  in¬ 
creasing.  By  this  factor  one  might  partly  explain  why  the  dif¬ 
ference  between  the  curves  for  100%  and  67%  learning  is  so 
meagre. 

But  one  cannot  explain  the  still  smaller  difference  between  the 
curves  for  150%  and  100%  learning  by  the  same  theory.  Fur¬ 
ther,  what  is  true  of  67%  learning  is  to  a  less  extent  also  true  of 
33%  learning.  The  difference  between  the  latter  and  all  the 
other  curves  is  the  greatest  of  all.  How  could  the  assumed  prac¬ 
tice  effect  have  influenced  33%  learning  so  differently? 

(2)  When  the  degree  of  learning  is  reduced  to  33%,  the 


THE  CONDITIONS  OF  RETENTION 


49 


amount  of  material  originally  learned  is  greatly  decreased.  One 
cannot  be  expected  to  retain  what  he  never  learned.  So  instead 
of  giving  the  amount  of  retention  for  33%  learning  as  a  per¬ 
centage  of  the  whole  syllable  series,  one  might  also  argue  that  it 
should  be  stated  as  a  percentage  of  the  number  of  syllables 
actually  learned. 

The  last  statement,  however,  amounts  to  saying  that  instead 
of  33%  or  67%  learning,  we  should  have  had  100%  learning. 
Doubtless  we  would  then  expect  the  resulting  retention  curve  to 
coincide  with  the  ordinary  retention  curve  for  100%  learning. 

In  fact,  the  number  of  syllables  actually  reported  is  a  very  poor 
measurement  of  the  degree  or  the  amount  of  learning.  The 
subject  was  required  to  learn  the  series  by  anticipation,  spelling 
the  syllables  aloud.  What  he  did  not  correctly  report  after  33% 
or  67%  learning  could  very  often  be  correctly  reproduced  even 
at  the  end  of  a  comparatively  long  interval.  This  phenomenon 
was  particularly  manifest  for  the  more  efficient  learners  who  re¬ 
quired  only  from  1  to  3  presentations  for  33%  learning.  The 
effect  of  the  last  presentation  in  the  original  learning  was  not 
brought  out  by  subsequent  anticipation.  When  the  total  number 
of  presentations  was  not  more  than  1  or  2,  this  last  effect  became 
increasingly  important.  Our  records  prove  that  the  ability  to 
recall  without  original  correct  anticipation  occurred  with  more  or 
less  frequency  for  all  the  subjects.  We  may  further  mention 
that  one  of  the  subjects  could  not  develop  the  habit  of  spelling 
aloud  what  he  learned  in  the  first  few  presentations. 

A  far  more  plausible  explanation  for  this  phenomenon  of 
diminished  return  is  that  the  effect  of  the  different  degrees  of 
learning  upon  the  amount  of  retention  follows  the  same  sequence 
as  does  the  learning  curve  for  memory.  If  negative  acceleration 
is  characteristic  of  the  acquisition  of  immediate  memory,  as  has 
been  repeatedly  proved,  one  may  assume  that  the  same  phe¬ 
nomenon  will  reappear  in  the  measurement  of  permanent  memory, 
which  differs  from  the  former  only  by  the  introduction  of  a 
longer  time  interval. 

From  the  shape  of  the  learning  curves  for  memory,  it  has 


50 


C.  W.  LUH 


been  concluded  that  the  phenomenon  of  diminished  returns  holds 
(i)  for  immediate  recall  and  (2)  for  all  degrees  of  learning  up 
to  100%.  We  can  now  state  in  the  light  of  our  data  that,  within 
the  limits  of  our  experiments,  this  phenomenon  also  holds  (1) 
for  delayed  recall  and  (2)  for  more  than  100%  learning. 

However,  even  on  this  theory  one  can  hardly  explain  the  nega¬ 
tive  differences  in  the  amounts  of  retention  between  150%  and 
100%  learning  for  certain  intervals.  In  Table  XV,  the  value 
for  150%  learning  is  lower  than  for  100%  learning  at  the  end 
of  1  and  2  days  for  written  reproduction;  at  the  end  of  2  days 
for  recognition;  at  the  end  of  1  day  for  reconstruction.  At  the 
end  of  2  days  for  reconstruction  the  values  for  the  two  curves  are 
practically  equal.  It  is  impermissible  to  extend  the  law  of  nega¬ 
tive  acceleration  to  cover  these  negative  cases.  One  can  hardly 
conceive  of  an  increase  of  50%  of  learning  as  resulting  in  an 
actual  decrease  in  the  amount  of  retention.  In  Chs.  IV  and  V 
we  shall  find  that  the  characteristic  deviations  for  150%  learning 
are  not  limited  to  these  unexpected  changes  in  the  amount.  There 
we  shall  offer  a  general  explanation  for  all  these  facts. 

With  the  exception  of  these  peculiarities  for  150%  learning, 
the  phenomenon  of  diminished  returns  seems  to  be  quite  as  gen¬ 
eral  for  delayed  recall  as  for  immediate  memory.  Naturally  one 
would  look  for  a  common  cause  for  both  phenomena  unless 
there  are  reasons  for  the  contrary.  We  further  maintain  that 
the  similarity  between  these  effects  is  not  a  coincidence,  but 
almost  a  mathematical  necessity.  Given  the  effect  of  diminished 
returns  in  the  curve  for  immediate  retention,  one  will  have  to 
make  some  wonderful  assumptions  for  not  expecting  the  same 
effect  to  appear  in  delayed  recall.  This  may  be  clearly  seen  in 
Fig.  X.  The  curves  presented  therein  are  hypothetical. 

When  the  phenomenon  of  diminished  returns  occurs  with  im¬ 
mediate  memory,  a  simple  way  to  state  this  fact  is  to  give  the  gen¬ 
eral  equation  of  the  curve,  y  =a  —  e— x.  When  nothing  is 
learned,  the  curve  passed  through  the  point  of  the  origin.  Hence, 

( 1 )  y  =  1  —  e— x. 

The  limit  of  y  will  be  1,  i.  e.,  the  mastery  of  100%  of  material 
regardless  of  the  degree  of  over-learning. 


THE  CONDITIONS  OF  RETENTION 


5i 


Supposing  that  the  phenomenon  of  diminished  returns  did 
not  reappear  in  delayed  recall,  the  curve  for  the  retention  values 
corresponding  to  various  degrees  of  learning  would  have  to  be 


either  a  straight  line  or  one  with  positive  acceleration.  For  the 
former,  we  have  the  equation  y  =  mx  +  b.  When  nothing 
is  learned,  nothing  is  retained.  Therefore, 

(2)  y  =  mx. 

When  the  value  of  m  is  properly  chosen,  the  curves  will  intersect 
with  each  other  as  in  the  figure. 

If  instead  of  linear  regression,  there  were  more  or  less  positive 
acceleration,  we  could  also  generalize  the  fact  by  stating  the 
equation. 

( 3 )  y  =  Ax  +  Bx2  +  Cx3  + . 

For  certain  values  of  the  constants  the  curves  (1),  (2)  and  (3) 
will  meet  at  the  same  point,  which  represents  that  for  practical 
purposes  the  material  is  so  well  mastered  that  there  can  be  no  fur¬ 
ther  forgetting. 

Now  if  we  compare  the  curves  between  this  point  of  intersec¬ 
tion  and  the  point  of  origin  by  mere  inspection,  it  becomes  clear 
that  for  whatever  values  of  the  constants,  the  maximum  differ¬ 
ence  between  (1)  and  either  (2)  or  (3)  will  not  occur  in  the 
immediate  neighborhood  of  either  of  the  points,  but  somewhere 
in  the  middle. 

Further,  curve  ( 1 )  is  fixed.  (2)  is  also  fixed  when  the  value 
of  m  is  determined.  Equation  (3)  is  an  endless  series,  x  is 
positive.  Assuming  all  the  constants  to  be  positive,  then  the 


52 


C.  IV.  LUH 


fewer  terms  we  take,  the  more  abrupt  will  be  the  change  in  curva¬ 
ture,  such  as  curve  (4)  in  the  figure. 

From  this  description  of  the  curves  one  can  see  that,  given 
the  effect  of  diminished  returns  in  the  learning  curve  for  memory, 
the  same  effect  will  not  appear  in  delayed  recall  only  on  one  of 
these  two  conditions. 

A.  A  certain  medium  degree  of  learning  is  the  least  effective 
with  respect  to  the  amount  of  retention.  This  amount  will  be 
increased  with  more  learning  and  also  with  less  learning.  Or 

B.  The  degree  of  learning  has  no  considerable  effect  upon  the 
amount  of  retention.  It  remains  very  meagre  for  all  degrees  of 
learning  until  the  latter  attains  a  critical  value  when  all  of  a 
sudden  the  amount  increases  to  nearly  100%  and  forgetting  dis¬ 
appears. 

Unless  and  until  either  one  of  the  conditions  is  empirically  ful¬ 
filled ,  the  conclusion  still  holds  true  that  the  phenomenon  of 
diminished  returns  is  general  for  both  immediate  and  delayed 
recall.  The  learning  curve  and  the  curve  constructed  on  the 
basis  of  the  diminishing  amounts  of  retention  due  to  different 
degrees  of  learning  are  related  to  each  other  somewhat  as  (1) 
and  (5).  In  the  latter,  the  parameter  assumes  the  value  a,  less 
than  unity. 

Ebbinghaus1  long  ago  discovered  this  tendency  of  diminished 
returns,  though  this  is  not  clearly  stated  in  his  monograph.  Thus 
he  found  that  the  amount  of  retention  after  one  day  was  a  func¬ 
tion  of  the  number  of  presentations  used  the  previous  day.  That 
number  was  varied  from  8  to  64,  by  intervals  of  8.  “For  each 
three  additional  repetitions  which  I  spent  on  a  given  day  on  the 
study  of  the  series,  I  saved,  in  learning  this  series  24  hours  later, 
on  the  average,  approximately  one  repetition;  and,  within  the 
limits  stated,  it  did  not  matter  how  many  repetitions  altogether 
were  spent  on  the  memorization  of  the  series.”  In  Sec.  34,  where 
he  treated  retention  as  a  function  of  repeated  learning,  he  con¬ 
cluded,  “The  effect  of  the  repetitions  is  at  first  approximately 
constant,  the  saving  which  results  from  these  repetitions  increases 
accordingly  for  a  while  proportional  to  their  number.  Gradually, 

1  Op.  cit.,  Ch.  VI,  Sec.  22-23  ’>  Ch.  VIII,  Sec.  34. 


THE  CONDITIONS  OF  RETENTION 


53 


the  effect  becomes  less;  and  finally,  when  the  series  has  become 
so  firmly  fixed  that  it  can  be  repeated  almost  spontaneously  after 
24  hours,  the  effect  is  shown  to  be  decidedly  less.” 

The  last  conclusion  quoted  above  is  self-evident,  and  clearly 
corroborates  our  results.  The  other  statements  may  be  mislead¬ 
ing.  When  the  effect  of  the  increase  in  the  degree  of  learning 
upon  the  amount  of  retention  is  said  to  be  “constant,”  or  to  in¬ 
crease  by  arithmetical  progression,  it  amounts  to  saying  that, 
according  to  his  “saving  method  ”  it  is  negatively  accelerative. 

100  (L— WL) 

The  formula  for  the  “saving  method”  is  Q  = - , 

L 

in  which  Q  is  the  percentage  of  saving,  L  the  time  required  for 
learning,  and  WL  the  same  for  relearning.  The  formula  holds 
when  L  is  equal  to  or  greater  than  WL.  When  such  is  the  case, 
a  constant  numerical  increment  to  both  the  numerator  and  the 

(L  +  3)-(WL-i) 

denominator  such  as  in  his  experiment, - , 

L  +  3 

(L  +  6)  —  (WL  — 2)  (L  +  9)  -  (WL  —  3) 

L  +  6  ’  L  +  9  ’ . . 

will  make  each  term  increase  in  value,  but  its  difference  from  the 
immediately  preceding  term  decrease  in  value.  The  effect  is  thus 
negatively  accelerative. 

When  L  is  smaller  than  WL,  as  in  incomplete  learning,  Eb- 
binghaus  used  as  a  basis  for  computation  the  hypothetical  L  that 
would  have  been  spent  had  it  not  been  for  the  previous  incom¬ 
plete  learning.  The  amount  of  saving  was  a  percentage  of  that 
hypothetical  L,  thus  neglecting  the  amount  of  time  that  was 
actually  spent  on  the  previous  day.  If  this  amount  of  time  had 
been  taken  into  consideration,  then  the  effect  of  the  increase  in 
the  degree  of  the  original  learning  upon  the  amount  of  retention 
could  be  shown  to  be  negatively  accelerative  throughout  his  in¬ 
vestigation. 

5.  A  Further  Word  Regarding  the  General  Shape  of  the 
Curves. 

In  the  last  chapter  the  difficulties  for  stating  a  general  equa¬ 
tion  which  would  satisfy  all  the  phenomena  of  forgetting  were 


54 


C.  IV.  LUH 


fully  elaborated.  The  reader  is  now  referred  to  Figs.  VII  to  IX. 
A  general  “logarithmic”  equation  must  make  allowance  for  the 
crossing  and  recrossing  of  the  “families”  of  written  reproduction 
and  reconstruction  curves.  Some  of  these  irregularities  may  in¬ 
deed  be  traced  back  to  inaccuracies  in  the  data  and  may  not  reap¬ 
pear  in  another  series  of  experiments  of  the  same  kind,  but  we 
maintain  that  any  mathematical  statement  of  the  Ebbinghaus 
tradition  will  require  more  experimental  background. 

Perhaps  the  most  embarrassing  group  of  curves  is  that  for 
recognition.  It  would  be  just  as  easy  to  fit  the  corresponding 
curves  of  forgetting  to  equations  of  the  first  degree  as  to  more 
complicated  logarithmic  equations.  These  curves  are  more  or 
less  parallel,  more  or  less  approaching  linear  regression,  and  as 
often  tending  to  positive  as  to  negative  acceleration.  One  thing 
we  can  definitely  state  is  that,  on  the  whole,  they  are  not  loga¬ 
rithmic. 

It  was  pointed  out  in  the  last  chapter  that  relearning  based  on 
the  “saving  method”  produces  a  type  of  curve  vastly  different 
from  the  results  of  the  other  methods  which  measure  the  amount 
of  reproduced  material.  Now  it  becomes  further  evident  that 
among  the  latter  group,  recognition  sometimes  has  its  unique 
curves  which  are  as  different  from  those  of  the  other  methods  as 
relearning  is  from  all  the  rest.  Under  certain  circumstances  it 
may  happen  that  each  of  these  curves  will  take  on  a  logarithmic 
form.  Strong’s  curve  for  recognition  memory,  for  instance,  is 
like  Ebbinghaus’  curve  for  the  “saving  method,”  and  the  former 
can  certainly  be  used  as  illustrative  of  Bean’s  generalized  state¬ 
ment.  We  do  not  maintain  that  relearning,  anticipation,  written 
reproduction,  recognition,  reconstruction,  etc.,  each  has  a  general 
curve.  We  only  indicate  that  the  logarithmic  assumption  and 
even  the  phenomenon  of  negative  acceleration  may  totally  dis¬ 
appear  upon  further  investigation. 

However,  if  the  problem  be  put  in  such  a  way  that  we  have  to 
choose  between  Ebbinghaus  and  Ballard,  then  the  former  type  of 
curve  is  much  closer  to  our  own  results. 


IV.  THE  EFFECT  OF  EXTENDING  THE  TIME  LIMIT 
FOR  RECALL  UPON  THE  AMOUNT  OF 
MATERIAL  RECALLED 

In  written  reproduction,  as  described  above,  a  record  was 
taken  at  the  end  of  the  first  minute  of  recall  and  another  at  the 
end  of  the  second  minute,  when  the  subject  did  not  finish  recall¬ 
ing  within  these  time  limits.  These  preliminary  records,  to¬ 
gether  with  the  other  records  which  were  completed  within  I 
or  2  min.,  may  be  taken  as  indicative  of  the  proficiency  of 
written  reproduction  memory  up  to  I  and  2  min.  of  recall  re¬ 
spectively. 

In  recognition  similar  preliminary  records  were  taken  at  the 
end  of  90  sec.  without  the  subject’s  knowledge.  The  difference 
between  these  90  sec.  records  and  the  complete  records  has  been 
referred  to  in  Ch.  II. 

We  present  in  Table  XVIII  the  comparative  results  for  the 
written  reproduction  methods  for  four  degrees  of  the  original 
learning.  The  values  for  100%  learning  are  averages  from  both 
series  of  experiments.  When  the  same  written  reproduction 
records  were  scored  for  position  and  sequence,  the  preliminary 
values  were  slightly  changed.  These  values  are  tabulated  in 
Table  XIX  to  facilitate  comparative  study.  Similar  results  for 
the  recognition  method  are  presented  in  Table  XX. 

1.  Comparison  of  the  Written  Reproduction  Results. 

It  was  indicated  in  connection  with  a  discussion  on  anticipa¬ 
tion  and  relearning  that  partial  retention  is  not  as  readily  recalled 
as  complete  retention.  Within  certain  limits,  the  duration  of 
the  recalling  process  may  directly  correspond  to  the  strength  of 
the  association.  However,  the  tendency  for  the  amount  of  recall 
to  increase  upon  extending  the  time  limit  very  soon  becomes  in¬ 
effective.  One  conclusion  we  can  draw  from  Tables  XVIII  and 
XIX  is  that  the  effect  of  extending  the  time  limit  for  recall  with 
the  written  reproduction  method  becomes  less  and  less  important 


55 


56 


C.  W.  LUH 


beyond  i  or  2  min.  The  extension  from  1  to  2  min.  increases 
the  scores  by  a  far  greater  amount  than  does  a  further  extension 
from  2  to  5  min.  This  particular  effect  is  quite  independent  of 
minute  variations  in  the  method  of  measurement.  Scoring  po¬ 
sition  and  sequence  does  not  in  the  least  change  the  relative  im¬ 
portance  of  the  successive  extensions  of  the  time  limit.  The 


TABLE  XVIII 

Written  Reproduction,  Comparison  of  Preliminary  and 

Final  Records 


20  min. 

1  h. 

2  h. 

3  h- 

4  h. 

6  h. 

12  h. 

1  day 

2  days 

150%  learning 

I  min . 

75-9 

60.0 

57-9 

43-0 

34-6 

26.0 

22.9 

Difference. . 

8.2 

16.5 

13.1 

13-7 

87 

57 

3-1 

2  min . 

84.1 

76.5 

71.0 

567 

43-3 

3i7 

26.0 

Difference. . 

39 

7-9 

10.9 

8.9 

11. 1 

6.8 

4-8 

Complete  . . . 

88.0 

844 

81.9 

65.6 

544 

38.5 

30.8 

Total  D.... 

12.1 

24.4 

24.0 

22.6 

19.8 

12.5 

7-9 

100%  learning 

1  min . 

75-6 

69.2 

44-3 

30.8 

26.4 

Difference. . 

10.5 

10.8 

II-5 

7-3 

3-8 

2  min . 

86.1 

80.0 

55-8 

38.1 

30.2 

Difference. . 

3-3 

4.0 

6.8 

4-3 

37 

Complete  .... 

89.4 

84.0 

62.6 

42.2 

33-5 

Total  D.... 

13.8 

14.8 

18.3 

11.6 

M 

67%  learning 

1  min . 

69.8 

477 

42.5 

3i7 

21.5 

Difference. . 

12.7 

14.0 

16.2 

6.6 

2.7 

2  min . 

82.5 

61.7 

58.7 

38.3 

24.2 

Difference. . 

2.9 

10.8 

7.i 

3-i 

.6 

Complete  _ 

854 

72.5 

65.8 

41.4 

24.8 

Total  D. ... 

15-6 

24.8 

23-3 

97 

3-3 

33%  learning 

1  min . 

59-8 

43-i 

31.2 

21.5 

12.7 

Difference. . 

6.2 

7-1 

8.8 

4-5 

4 

2  min . 

66.0 

50.2 

40.0 

26.0 

13.1 

Difference. . 

1-7 

3-8 

2.7 

.2 

.6 

Complete  _ 

67.7 

54-o 

42.7 

26.2 

137 

Total  D.... 

7-9 

10.9 

ii.5 

47 

1.0 

latter  also  holds  for  all  degrees  of  the  original  learning  except 
for  the  12-hr.,  i-day  and  2-day  intervals  with  150%  learning. 
In  these  exceptional  cases  the  second  extension  of  three  minutes 
seems  to  be  more  effective  than  the  first  extension  of  one  minute. 
Two  of  these  intervals,  1  day  and  2  days,  correspond  to  the  points 


THE  CONDITIONS  OF  RETENTION 


57 


TABLE  XIX 

Written  Reproduction,  Comparison  of  Preliminary  and  Final 
Records,  Scoring  Position  and  Sequence 


20  min. 

1  h. 

2  h. 

3  h- 

4  h. 

6  h. 

12  h. 

1  day 

2  days 

150%  learning 

1  min . 

72.4 

56.7 

53-3 

38.2 

324 

22.9 

20.0 

Difference. . 

8.5 

16.4 

11  -7 

12.5 

8.2 

4-3 

1.8 

2  min . 

80.9 

73.1 

65.0 

50.7 

40.6 

27.2 

21.8 

Difference. . 

3-8 

9-3 

10.0 

7-9 

10.1 

5-0 

24 

Complete  .... 

84.7 

82.4 

75-0 

58.6 

50.7 

32.2 

24.2 

Total  D.... 

12.3 

257 

21.7 

204 

18.3 

9-3 

4.2 

100%  learning 

1  min . 

71. 1 

644 

394 

26.3 

22.9 

Difference. . 

94 

8.9 

9.0 

5-7 

3-0 

2  min . 

80.5 

73-3 

48.4 

32.0 

25.9 

Difference. . 

2.9 

3-9 

5-8 

3-0 

2.2 

Complete  .... 

834 

77.2 

54.2 

35-° 

28.1 

Total  D.... 

12.3 

12.8 

14.8 

8-7 

5-2 

67%  learning 

1  min . 

65.1 

42.0 

364 

26.1 

17.2 

Difference. . 

12.8 

12.5 

13.6 

5-2 

2.5 

2  min . 

77-9 

54.5 

50.0 

3i-3 

19.7 

Difference. . 

2.6 

9.6 

74 

2.2 

•3 

Complete  _ 

80.5 

64.1 

574 

33-5 

20.0 

Total  D... 

154 

22.1 

21.0 

74 

2.8 

33%  learning 

1  min . 

53.3 

37-7 

26.2 

1 7-7 

9-5 

Difference. . 

6.1 

5-7 

6.8 

3-6 

.2 

2  min . 

594 

434 

33-o 

21.3 

97 

Difference. . 

1-3 

4.2 

2.2 

.2 

.8 

Complete  . . . . 

60.7 

47.6 

35*2 

21.5 

10.5 

Total  D.... 

74 

97 

9.0 

3-8 

1.0 

where  the  retention  values  for  the  1 50%  learning  curve  decrease 
very  rapidly,  as  noticed  in  the  last  chapter.  The  facts  still  await 
an  explanation,  but  we  shall  have  to  postpone  further  discussion 
to  the  end  of  Ch.  V. 

With  increase  in  the  length  of  the  time  interval,  the  same  de¬ 
cline  in  the  effect  of  extending  the  time  limit  is  also  observed. 
Previous  to  the  lapse  of  the  4-hr.  interval,  the  increment  due  to 
extending  the  time  limit  grows  larger  and  larger.  It  then  sud¬ 
denly  decreases  with  time.  This  characteristic  change  of  the  in¬ 
crement  prevails  under  various  conditions.  It  holds  for  all  de¬ 
grees  of  learning.  It  is  not  altered  by  scoring  position  and  se- 


58 


C.  W.  LUH 


■  TABLE  XX 

Recognition,  Comparison  of  Preliminary  and  Final  Records 


20  min. 

1  h. 

2  h. 

3  h* 

4  h. 

6  h. 

12  h. 

1  day  2  days 

150%  learning 

90  sec . 

967 

94.1 

91. 1 

9i.5 

88.7 

85.8  72.8 

Complete  .... 

97-5 

95-8 

93-3 

91.6 

92.5 

83.2  72.8 

Difference. . 

.8 

17 

2.2 

.1 

3-8 

— 2.6  .0 

100%  learning 

90  sec . 

957 

93-8 

9i-5 

71.2  69.4 

Complete  - 

96.8 

94.8 

927 

76.1  75-2 

Difference. . 

1. 1 

1.0 

1.2 

4*9  5-8 

67%  learning 

90  sec . 

92.9 

94.6 

85.2 

72.6  61.5 

Complete  .... 

93-2 

93-3 

847 

737  61.5 

Difference. . 

•3 

—i-3 

—•5 

1. 1  .0 

33%  learning 

90  sec . 

75-0 

66.0 

54-3 

44-6  294 

Complete  .... 

73.3 

64.4 

54-6 

457  25.5 

Difference. . 

—17 

— 1.6 

•3 

1.1  —3.9 

quence,  nor  is 

it  minimized  when  the  increment 

is  computed  as 

a  percentage  of  the  total  score. 

The  strength  of  retention  for  the  different  syllables  is,  there¬ 
fore,  not  equal.  Some  are  more  easily  recalled  than  others,  and 
consequently  take  less  time.  When  the  time  interval  is  length¬ 
ened,  the  more  difficult  and  uncertain  ones  deteriorate  first.  The 
amount  of  this  partial  retention  increases  in  value  for  the  first 
few  hours  after  learning.  Thereafter,  not  only  does  retention 
as  a  whole  deteriorate  with  time,  but  the  strength  and  the  amount 
of  partial  retention  also  decrease  so  that  its  re-instatement  upon 
the  extension  of  the  time  limit  becomes  less  and  less  probable. 
The  assumption  as  presented  in  Ch.  II  which  states  that  the 
amount  of  partial  retention  increases  with  the  time  interval  for 
all  memory  processes  is  evidently  unsound. 

We  can  mention  the  fact  in  this  connection  that  from  4  hours 
to  1  day  is  a  long  interval,  and  that  in  the  latter  case,  sleep  occurs 
between  learning  and  relearning.  Increase  in  the  degree  of  the 
original  learning  seems  to  arrest  this  change  in  the  magnitude  of 
the  increment,  though  very  ineffectively.  Thus,  with  150% 
learning  there  seems  to  be  a  plateau  in  the  effect  of  extending 
the  time  limit  for  the  intervals  from  3  to  12  hours  inclusive,  and 


THE  CONDITIONS  OF  RETENTION 


59 


then  the  sudden  decrease.  This  would  mean  that  the  growth  of 
the  total  amount  of  forgetting  is  arrested  to  that  extent.  In 
100%,  67%  and  33%  learning,  the  abruptness  of  that  change 
which  occurs  at  the  lapse  of  the  4-hr.  interval  to  the  increment 
resulting  from  longer  durations  of  the  recalling  process  is  also 
somewhat  proportional  to  the  degree  of  the  original  learning. 

2.  Comparison  of  the  Recognition  Results. 

Coming  now  to  recognition,  the  effect  of  extending  the  time 
limit  beyond  90  sec.  is  quite  different  from  the  results  we  just 
discussed.  In  some  respects,  the  conclusions  from  these  two 
methods  of  measurement  are  contradictory.  If  we  can  directly 
compare  the  magnitude  of  the  scores,  the  increment  for  recogni¬ 
tion  is  very  much  smaller.  But  a  more  significant  contrast  is  that, 
with  100%  learning,  the  increment  for  recognition  is  almost  con¬ 
stant  in  value  until  the  lapse  of  the  4-hr.  interval,  and  then  sud¬ 
denly  increases  for  the  i-day  interval  and  becomes  still  higher 
at  the  end  of  2  days.  This  contradicts  what  we  have  found  in 
written  reproduction  in  every  particular.  Assuming  that  partial 
retention  takes  more  time  for  recall,  as  we  have  done,  these  char¬ 
acteristics  of  the  recognition  process  seem  to  corroborate 
Strong’s2  conclusion  which  maintains  that  in  recognition  memory 
the  amount  of  partial  recognitions  does  not  decrease  in  time  as 
fast  as  the  amount  of  recognition  as  a  whole.  One  may  even 
conclude  that  the  partial  recognitions  actually  increase  with  the 
length  of  the  interval. 

With  150%  learning  there  seems  to  be  a  general  increase  of 
the  effect  of  extending  the  time  limit  upon  the  amount  of  recog¬ 
nition  until  the  lapse  of  the  12-hr.  interval.  At  that  point  the 
increment  disappears.  The  subjects  seemed  to  have  selected  all 
the  syllables  they  could  recognize  at  the  end  of  90  sec.,  the  rest  of 
the  process  being  chance  performance.  It  is  difficult  to  think  of 
an  increase  of  50%  in  the  original  learning  as  affecting  a  de¬ 
crease  in  the  amount  of  recognition.  A  tentative  explanation  of 
this  fact  will  be  presented  at  the  end  of  Ch.  V. 

For  67%  and  33%  learning,  there  is  no  sudden  change  of 

2  Op.  Cit.,  pp.  352  ff. 


6o 


C.  W.  LUH 


the  increment  as  with  150%  Extending  the  time  limit  for  recog¬ 
nition  does  not  result  in  any  appreciable  change  in  the  numerical 
values  either  way,  except  that  at  the  end  of  the  2-day  interval  for 
33%  learning,  it  affects  a  considerable  decrease  in  the  total  score. 
This  is  to  be  expected  if  we  remember  that  finally  the  amount  of 
partial  recognition  may  itself  decrease  so  that  even  the  presenta¬ 
tion  of  the  original  material  does  not  avail.  Nevertheless,  the 
subject  was  required  to  complete  the  selection  of  12  syllables,  de¬ 
pending  upon  chance;  hence,  there  was  a  decrease  in  the  total 
score.  This  final  decrease  in  the  amount  of  partial  recognition 
is  also  hastened  by  a  less  complete  degree  of  learning.  Thus, 
while  the  numerical  value  for  the  2-day  interval  with  67%  learn¬ 
ing  is  not  changed  by  the  extension  of  the  time  limit  for  recall, 

the  corresponding  score  was  decreased  by  3.9  with  33%  learning. 
* 

3.  The  Gradation  of  the  Memory  Processes. 

The  results  from  both  methods  of  measurement  seem  to  in¬ 
dicate  that  written  reproduction  and  recognition  memory  are 
quite  different,  but  the  difference  is  still  one  of  degree,  not  of 
kind.  One  process  may  pass  over  to  the  other.  Judging  from 
commonsense,  recognition  memory  lasts  longer  than  the  ability 
to  reproduce  ad  verbatim.  What  fails  even  the  vaguest  recall 
may,  upon  the  presentation  of  the  object,  flash  into  distinct  recog¬ 
nition.  On  the  other  hand,  if  enough  time  be  allowed,  one  can 
as  a  rule  recognize  what  he  can  recall.  It  seems  that  the  memory 
processes  are  graded  in  some  such  way  as  the  following : 

A.  Complete  retention. 

B.  Partial  retention,  which  takes  time  for  recall,  and  may 

involve  errors,  as  will  be  seen  in  another  chapter. 

C.  Still  less  permanent  retention  which  may  completely 

escape  written  reproduction,  but  which,  nevertheless, 
may  be  reinstated  in  recognition. 

D.  Partial  recognition  memory  which  can  be  developed  upon 

extending  the  time  limit  for  recall. 

E.  Retention  that  cannot  be  measured  even  by  the  method 

of  recognition.  It  approaches  complete  obliviscence 
and  occurs  at  the  end  of  a  fairly  long  interval  after 
incomplete  learning. 


THE  CONDITIONS  OF  RETENTION 


61 


Condition  A  gives  place  to  B  soon  after  learning,  at  least  with 
a  great  part  of  the  retained  material.  Thereafter  B  approaches  C 
faster  than  A  does  B  so  that  the  total  amount  of  B  decreases 
with  the  lapse  of  the  4-hr.  interval.  C  lasts  for  a  long  time  and 
gives  place  to  D.  D  is  not  effective  upon  the  immediate  presenta¬ 
tion  of  the  original  material,  but  may  return  in  the  process  of 
recognition.  When  the  degree  of  the  original  learning  is  only 
33%,  the  amount  of  D  becomes  insignificant  at  the  end  of  2 
days.  The  paradoxical  effect  is  to  shorten  the  duration  of  the 
actual  process  of  recognition  to  less  than  90  sec.  when  the  syl¬ 
lables  that  can  be  recognized  have  all  been  selected,  but  ap¬ 
parently  to  increase  the  duration  beyond  that  time  limit.  Nothing 
being  remembered,  the  extended  time  serves  only  to  fulfill  the 
requirement  of  the  experiment,  which  is  to  select  12  syllables. 

4.  The  Effect  of  Extending  the  Time  Limit  upon  the  Shape  of 
the  Curves  of  Retention. 

( 1 )  In  written  reproduction  the  curve  changes  with  the  mag¬ 
nitude  of  the  increment  resulting  from  extending  the  time  limit 
to  5  min.  As  compared  with  the  preliminary  curve  for  the  1-  or 
2-min.  records,  the  final  curve  falls  more  gradually  within  the 
first  four  hours  after  learning,  and  then  more  suddenly.  If  the 
preliminary  curve  of  forgetting  be  logarithmic,  the  effect  of  the 
increment  would  at  least  tend  to  complicate  the  function. 

(2)  In  recognition  with  67%  learning,  the  more  gradual  fall 
of  the  curve  owing  to  the  extension  of  the  time  limit  continues 
until  the  end  of  the  second  day. 

(3)  In  recognition  with  67%  and  33%  learning,  extending  the 
time  limit  does  not  bring  about  any  appreciable  change  in  the 
curves. 

(4)  The  shapes  of  the  curves  are  practically  determined  for 
written  reproduction  at  the  end  of  2  min.  and  for  recognition  at 
the  end  of  go  sec. 


V.  THE  RELATION  BETWEEN  THE  AMOUNT  OF 
ERROR  AND  OTHER  FACTORS 


In  the  recognition  and  reconstruction  methods  of  measurement, 
the  score  was  determined  directly  by  the  amount  of  error  made 
in  recall  as  well  as  by  the  amount  of  correct  material.  With  the 
“saving  method”  the  number  of  presentations  required  for  re¬ 
learning  was  determined  by  the  amount  of  forgetting,  but  inci¬ 
dentally  also  by  the  amount  of  error.  But  errors  were  disre¬ 
garded  in  the  scores  for  anticipation  and  written  reproduction. 
An  attempt  to  keep  separate  records  for  the  number  of  incorrect 
responses  in  anticipation  met  with  failure.  The  duration  of 
recall  for  each  syllable  was  too  short,  considering  the  fact  that 
the  experimenter  already  had  to  turn  the  drum  and  to  record 
success  or  ^failure  between  responses.  In  written  reproduction, 
however,  the  records  were  permanent  and  we  could  study  the 
amount  and  nature  of  error  after  the  experiments  were  com¬ 
pleted. 

i.  The  Amount  of  Error  as  a  Function  of  the  Length  of  the 
Interval. 

The  amount  of  error  made  in  written  reproduction  for  each 
time  interval  and  each  degree  of  learning  is  presented  in  Table 
XXL  With  the  possible  exception  of  33%  learning,  the  amount 
of  error  increases  with  the  length  of  the  interval. 

TABLE  XXI 

Amount  of  Error  in  Written  Reproduction 

20  min.  1  hr.  2hrs.  3  hrs.  4hrs.  6hrs.  I2hrs.  id.  2d. 


150%  learning...  2.7  3.1  6.7  7.3  8.3  12.9  15.8 

Joo%  .  4-2  5-8  11 .7  11.7  11.3 

67%  .  3-3  4-6  5.4  7.7  9.o 

33%  .  4-4  7-9  10.8  5.2  8.7 


p.  The  Relation  between  the  Amount  of  Error  and  the  Degree 
of  Learning. 

In  Table  XXI  the  amount  of  error  for  150%  learning  is  prob¬ 
ably  smaller  than  for  any  other  degree  of  learning  with  the 

62 


THE  CONDITIONS  OF  RETENTION 


63 


shorter  intervals,  but  it  grows  to  be  the  largest  when  the  interval 
is  lengthened. 

On  the  whole,  error  does  not  seem  to  be  proportional  to  the 
degree  of  learning  until  the  lapse  of  the  4-hr.  interval.  There¬ 
after  the  gross  amount  of  error  increases  with  the  degree  of 
learning. 

These  facts  may  be  compared  with  the  effect  of  extending  the 
time  limit  upon  the  amount  of  reproduction,  as  discussed  in  Ch. 
IV.  The  magnitude  of  that  effect  for  150%  learning  changes 
from  the  shorter  to  the  longer  intervals  in  the  same  manner  as 
does  the  amount  of  error.  Before  the  lapse  of  the  4-hr.  interval 
also,  that  effect  is  not  proportional  to  the  degree  of  learning,  but 
the  two  factors  take  on  a  functional  relationship  for  the  i-day 
and  2-day  intervals.  So  the  relationship  between  learning  and 
error  is  similar  to  the  relationship  between  learning  and  the 
effect  of  extending  the  time  limit.  However,  the  latter  effect 
decreases  with  the  lapse  of  the  4-hr.  interval,  while  the  amount 
of  error  increases  with  the  time  interval  to  the  end  of  2  days. 

As  already  explained,  the  effect  of  extending  the  time  limit  is  a 
function  of  the  amount  of  partial  retention.  It  is  proportional 
to  the  amount  of  retention  of  condition  B  (p.  60)  which  can  be 
reinstated  in  written  reproduction  but  which  takes  time.  Now  we 
are  ready  to  state  a  theory  as  to  the  significance  of  error  making, 
and  to  see  how  it  can  be  applied  to  explain  the  facts  enumerated. 
The  condition  of  error  making  is  not  complete  forgetting  or  ob- 
liviscence.  It  is  the  presence  of  partial  retention  which  can 
hardly  be  reinstated  but  which,  nevertheless,  is  so  near  the  point 
of  complete  recall  as  to  cause  conflict  and  confusion.  Errors  are 
made  mostly  in  the  change  from  condition  B  to  C. 

Thus,  with  150%  learning,  on  account  of  the  higher  degree  of 
original  mastery,  the  amount  of  partial  retention  of  condition 
B  is  small  as  compared  with  that  of  A.  The  amount  that  is  due 
to  the  change  from  condition  B  to  C  is  also  insignificant.  Hence, 
we  have  the  smaller  amount  of  error  for  the  short  intervals. 
When  the  time  interval  is  lengthened,  condition  B  prevails  and 
the  amount  of  error  increases  steadily. 


64 


C.  W.  LUH 


Similarly,  we  can  explain  why  the  amount  of  error  is  parallel 
to  the  effect  of  extending  the  time  limit  in  almost  every  instance. 
The  two  are  reciprocal  functions  and  both  are  due  to  the  exist¬ 
ence  of  partial  retention.  Eventually  the  amount  of  error  will 
decrease  with  the  amount  of  partial  retention,  but  the  former 
may  keep  on  increasing  while  the  effect  of  extending  the  time  limit 
has  reached  a  climax.  The  amount  of  error  increases  because 
condition  B  approaches  C  much  nearer  for  the  longer  intervals 
than  for  the  shorter  ones.  Therefore,  the  increase  in  score  due 
to  extending  the  time  limit,  plus  the  amount  of  error,  is  an  ap¬ 
proximation  of  the  amount  of  partial  retention.  The  change 
from  condition  B  to  C  is  a  very  complicated  process. 

j.  The  Relation  between  the  Amount  of  Error  and  the  Amount 
of  Retention. 

When  the  time  interval  is  lengthened,  retention  decreases  but 
error  increases.  So  if  the  amount  of  error  is  calculated  as  a  per¬ 
centage  of  the  amount  of  retention,  the  values  will  increase  more 
rapidly.  The  significance  of  this  comparison  is  questionable. 
The  amount  of  error  should  rather  be  compared  with  the  amount 
of  forgetting,  the  whole  syllable  series  minus  the  amount  of  re¬ 
tention,  which  therefore  increases  with  the  time  interval. 

4.  The  Relation  between  the  Amount  of  Error  and  the  Amount 
of  Forgetting. 

The  comparative  data  for  the  amount  of  forgetting  and  of 
error  are  presented  in  Table  XXII. 

The  increase  with  the  time  interval  in  the  amount  of  error  is 
much  slower  relative  to  the  increase  in  the  amount  of  forgetting. 
This  difference  in  the  rate  of  increase  with  the  time  interval  is 
further  inversely  proportional  to  the  degree  of  learning. 

As  already  stated,  errors  are  made  mostly  in  the  transition  from 
condition  B  to  C,  and  the  partial  retention  that  cannot  be  even 
thus  reinstated  is  apparently  forgotten,  according  to  the  written 
reproduction  method  of  measurement.  So  with  the  increase  in 
the  time  interval,  the  amount  of  forgetting  has  a  higher  accumu¬ 
lative  value  than  is  possible  to  the  amount  of  error.  The  former 
naturally  increases  more  rapidly.  Further,  if  a  higher  degree  of 


THE  CONDITIONS  OF  RETENTION 


65 


TABLE  XXII 

Comparison  of  the  Amount  of  Forgetting  and  of  Error  in 

Written  Reproduction 

20  m.  1  h.  2  h.  3  h.  4  h.  6  h.  12  h.  id.  2  d. 


150%  learning 

Forgetting  -  12.0  15.6  18.1  34.4  45.6  61.5  69.2 

Error  .  2.7  3.1  6.7  7.3  8.3  12.8  15.8 

iro%  learning 

Forgetting  ....  9.4  14.2  35.2  54.4  59.8 

Error  .  4.2  5.8  11.7  11.7  11.3 

67%  learning 

Forgetting  ....  14.6  27.5  34.2  58.5  75-2 

Error  .  3.3  4.6  5.4  7.7  9.0 

33%  learning 

Forgetting  ....  32.3  46.0  57.3  73.8  86.3 

Error  .  4.4  7.9  10.8  5.2  8.7 


learning  tends  to  arrest  the  whole  process  of  forgetting,  then  the 
difference  between  the  increase  in  the  amount  of  forgetting  and 
of  error  will  be  inversely  proportional  to  the  degree  of  learning. 

Aside  from  these  general  statements,  the  relationship  between 
error  and  forgetting  is  obscure.  With  150%  learning,  the 
amount  of  forgetting  is  to  the  amount  or  error  as  5  is  to  1,  for 
all  the  time  intervals.  This  ratio  regularly  decreases  with  the 
time  interval  when  the  degree  of  learning  is  reduced  to  67%. 
With  the  other  degrees  of  learning,  there  is  no  definite  relation¬ 
ship.  The  P.E.’s  of  the  values  that  constitute  the  curve  for 
the  amount  of  error  are  too  high  to  give  warrant  to  further 
generalization. 

However,  this  lack  of  similarity  or  causal  relationship  be¬ 
tween  the  two  groups  of  values  only  intensifies  the  problem.  The 
amount  of  error  is  indicative  of  the  amount  of  partial  retention. 
In  other  words,  the  curve  for  the  amount  of  error  is  a  part  and 
parcel  of  the  curve  of  forgetting.  Upon  the  evaluation  of  this 
relationship  will  depend  whether  a  universal  mathematical  state¬ 
ment  of  the  problem  is  possible. 

The  Effects  of  150%  Learning  upon  Various  Factors 

From  the  above  section,  it  is  found  that  the  relationship  be¬ 
tween  forgetting  and  error  is  more  definite  for  150%  than  for 
any  other  degree  of  learning.  The  ratio  of  the  two  amounts  does 


66 


C.  W.  LUH 


not  decrease  with  the  time  interval  as  it  does  with  lower  degrees 
of  learning.  We  are  now  ready  to  gather  together  what  has 
been  noticed  in  the  last  two  chapters  concerning  the  character¬ 
istics  of  150%  learning. 

1)  Its  retention  values  are  lower  than  for  100%  learning  at 
the  end  of  1  and  2  days  in  written  reproduction,  at  the  end  of 
1  day  in  reconstruction  and  at  the  end  of  2  days  in  recognition 

(p-  50). 

2)  The  effect  of  extending  the  time  limit  upon  the  amount  of 
written  reproduction  is  peculiar  in  this  case.  A  second  extension 
of  the  time  limit  from  2  to  5  min.  brings  about  a  larger  incre¬ 
ment  than  the  first  extension  from  1  to  2  min.  This  relative 
effectiveness  of  the  two  extensions  of  the  time  limit  is  just  the 
reverse  of  what  has  been  found  with  all  other  degrees  of  learn- 
>ng  (p.  56)- 

3)  Extending  the  time  limit  for  recognition  gives  negative 
results  at  the  end  of  the  1-  and  2-day  intervals.  The  effect  of 
the  extension  is  different  for  the  shorter  intervals  with  the  same 
degree  of  learning  and  for  all  the  intervals  with  100%  learning 

(P-  59)- 

An  explanation  for  these  peculiarities  is  possible  under  the  fol¬ 
lowing  suppositions. 

A)  A  high  degree  of  learning,  as  we  have  indicated,  tends  to 
arrest  the  process  of  forgetting.  In  the  process  of  forgetting,  re¬ 
tention  of  condition  A  approaches  partial  retention  of  condition 
B,  the  latter  approaches  C,  etc. 

B)  Most  of  the  syllable  series  for  100%  learning  were  given 
each  subject  before  the  150%  series.  In  the  former  experiments 
they  had  noticed  that  the  amount  of  retention  after  1  or  2  days 
was  comparatively  low.  This  fact  might  have  influenced  their 
attitude  when  they  came  to  the  longer  intervals  in  1 50%  learning. 

Combining  these  two  postulates,  it  seems  probable  that  for 
the  longer  intervals  there  may  be  a  conflict  of  condition  B  with 
both  A  and  C,  when  B  is  intensified  with  over-learning.  The 
retroactive  effect  is  (1)  to  decrease  the  total  amount  of  written 
reproduction.  (2)  It  naturally  follows  that  the  effect  of  the 


THE  CONDITIONS  OF  RETENTION 


67 


second  extension  of  the  time  limit  will  be  greater  than  that  of 
the  first,  for  the  conflict  will  tend  to  prolong  the  recall  process  of 
even  the  well  retained  members.  (3)  And  as  condition  B  always 
approaches  C  and  also  conflicts  with  C,  the  amount  of  error  will 
be  increased  for  the  longer  intervals. 

Even  on  this  hypothetical  basis,  there  is  no  explanation  for 
the  sudden  drop  of  the  retention  curve  for  recognition  at  the  end 
of  2  days.  In  the  same  connection  the  extension  of  the  time 
limit  gives  negative  results.  Probably,  over-learning  causes  a 
part  of  the  syllable  series  to  stand  out  more  distinctly,  thus  con¬ 
trasting  with  the  relative  ‘"amnesia”  of  the  other  parts. 

Were  these  explanations  unsatisfactory,  the  fact  remains  con¬ 
clusive  that  over-learning  to  the  extent  of  150%  is  at  less  ad¬ 
vantage  than  100%  learning  when  tested  for  retention  at  the  end 
of  1  and  2  days. 


VI.  THE  DURATION  AND  THE  SPEED  OF  THE 
PROCESS  OF  RECALL  IN  WRITTEN  REPRODUC¬ 
TION,  RECOGNITION  AND  RECONSTRUCTION 

Two  scores,  one  of  amount  and  one  of  time,  are  not  mutually 
interpretative,  but  the  latter  may  in  a  way  be  indicative  of  the 
nature  and  the  strength  of  retention,  though  not  in  quantitative 
terms.  The  data  thus  far  presented  all  concern  the  amount  of 
retention,  correctly  or  incorrectly  reproduced.  In  Ch.  IV  we  dis¬ 
cussed  the  effect  of  different  time  limits  only  in  relation  to  the 
amount  of  reproduced  material.  We  can  now  consider  the  dura¬ 
tion  and  the  speed  of  the  process  of  recall  with  the  different 
methods  of  measurement. 

The  “saving  method”  does  not  give  separate  measurements  for 
time  and  amount,  so  the  two  cannot  be  independently  treated. 
The  duration  or  the  speed  of  the  anticipation  process  is  not  sig¬ 
nificant,  its  value  being  a  constant,  2  sec.  for  each  syllable. 

With  the  other  three  methods  of  measurement,  duration  and 
speed  are  quite  independent  of  the  amount  of  retention.  In 
written  reproduction  the  subject  could  take  any  length  of  time 
up  to  5  min.  As  a  rule,  he  did  not  take  as  long  as  5  min.  to 
finish  the  process.  In  recognition  and  reconstruction,  there  was 
not  even  a  time  limit.  So  the  relationship  between  the  time  and 
the  amount  of  recall  becomes  an  important  problem. 

1.  Duration  as  a  Function  of  the  Order  in  which  the  Measure¬ 
ments  were  T aken. 

In  Table  XXIII  are  presented  the  average  durations  of  the 
three  processes  of  recall  in  number  of  seconds. 

From  Table  XXIII,  written  reproduction  had  the  longest  dura¬ 
tion,  recognition  the  second  and  reconstruction  the  last.  That 
was  exactly  the  order  in  which  the  measurements  were  taken, 
written  reproduction  being  the  first,  recognition  the  second  and 
reconstruction  the  last. 


68 


THE  CONDITIONS  OF  RETENTION 


69 


TABLE  XXIII 

Duration  of  Recall,  No.  of  Sec. 

20  m.  1  h.  2  h.  3  h.  4  h.  6  h.  12  h.  id.  2  d. 


Writ.  Reprod. 

150%  learning  134.4  I7I-4  193-8  209.5  198.6  186.4  178.7 

*100%  A .  1 12.2  134.0  147.9  132.1  97-0 

100%  B .  145.5  171.2  211.6  182.7  176.0 

67%  139.0  207.4  189.3  157-5  154-6 

33%  108.8  155.1  124.2  108.3  101.4 

Recognition 

150%  learning  60.6  71.7  81.8  94.3  99.9  86.9  114.2 

*100%  A .  76.7  87.1  1 08. 1  126.9  132.8 

100%  B .  72.6  78.4  92.6  89.9  101.3 

67%  68.9  83.2  98.9  92.7  107.9 

33%  88.4  104.0  100.6  93.1  1 14.0 

Reconstruction 

150%  learning  29.5  32.3  41.0  50.2  51. 1  61.4  60.2 

*100%  A .  47-9  4i-9  50.4  62.3  68.7 

100%  B .  50.0  41. 1  45-3  57-9  59-2 

67%  37-5  53-2  48.2  58.0  57-8 

33%  43-7  44-5  52.3  48.1  5i-7 


*A  The  first  series  of  experiments. 

B  The  second  series  of  experiments. 

The  duration  of  written  reproduction  was  shorter  in  the 
first  series  of  experiments  than  in  the  second  series,  but  the  com¬ 
parative  duration  of  recognition  was  vice  versa.  No  important 
difference  between  the  two  series  of  experiments  was  recorded 
in  reconstruction. 

So  the  difference  in  duration  may  have  incidentally  resulted 
from  the  technique  of  the  experiments,  quite  independent  of  the 
relative  difficulty  of  the  processes.  Each  recall  process  may  have 
facilitated  the  succeeding  one.  The  longer  the  written  reproduc¬ 
tion  process,  for  instance,  the  shorter  was  the  duration  of  recog¬ 
nition.  However,  as  we  have  seen  in  Ch.  II,  the  conditions  of 
recall  differed  in  the  number  of  restricting  factors  involved. 
Most  probably,  these  factors  also  influenced  the  duration  of  the 
processes. 

7.  The  Speed  of  Recall. 

The  recognition  and  reconstruction  methods  of  measurement 
required  the  subject  to  complete  the  process  of  recall  regardless 
of  the  amount  of  correct  retention.  So  with  these  two  methods, 


70 


C.  W.  LUH 


the  duration  and  the  speed  of  recall  are  identical.  The  condi¬ 
tions  were  very  different  in  written  reproduction.  There  the 
subject  could  “give  up”  at  any  time.  The  averages  presented  in 
Table  XXIII  fall  far  below  the  limit  of  5  min.  The  average 
subject  would  “give  up”  long  before  the  lapse  of  that  time  limit. 
At  the  same  time,  the  amount  of  reproduction  varied  with  the 
amount  of  retention,  and  the  differences  in  duration  might  simply 
be  in  part  a  function  of  the  amount  of  material  that  was  repro¬ 
duced. 

To  avoid  this  difficulty,  the  speed  of  written  reproduction  is 
calculated  as  the  number  of  seconds  per  unit  material.  If  the  dura¬ 
tion  of  recall  varied  only  as  an  effect  of  the  amount  of  reproduc¬ 
tion,  then  the  speed  per  unit  would  have  a  constant  value  for  all 
the  intervals.  Such,  however,  is  not  the  case,  as  may  be  seen  in 
Table  XXIV. 

TABLE  XXIV 

Speed  of  Reproduction,  No.  of  Sec.  per  Unit  Material 

20  m.  1  h.  2  h.  3  h.  4  h.  6  h.  12  h.  id.  2  d. 


150%  learning  1.9  2.4  2.6  4.2  4.8  6.9  8.6 

100%  .  1.7  1. 1  3.8  6.0  7.3 

67% .  1.8  3.5  4.4  6.3  9.3 

33% .  i-8  3-2  3-6  6.1  11. 1 


Comparing  that  table  with  the  recognition  and  reconstruction 
values  in  Table  XXIII  (except  the  data  from  the  1st  series  of 
experiments),  the  relationship  between  the  speed  of  recall  and 
other  factors  may  be  summarized  as  follows : 

(/)  The  speed  of  recall  decreases  with  the  time  interval. 
This  generalization  holds  for  written  reproduction  without  ex¬ 
ception.  That  such  a  tendency  exists  in  recognition  is  also  un¬ 
questionable.  With  reconstruction,  the  difference  in  speed  be¬ 
tween  the  1 -day  and  2-day  intervals  is  very  slight,  and  there  are 
also  marked  deviations  from  the  assumed  functional  relation¬ 
ship  for  the  shorter  intervals.  But  the  decrease  in  speed  with 
time  may  be  clearly  seen  if  we  taken  the  average  of  all  the  de¬ 
grees  of  learning. 

(2)  On  the  zvhole,  the  speed  of  recall  increases  with  the  degree 
of  learning. 

(j)  Since  the  duration  of  recognition  and  reconstruction  in- 


THE  CONDITIONS  OF  RETENTION 


7 1 


creases  with  the  time  interval,  while  the  amount  retained  and  the 
accuracy  of  the  two  processes  decrease  with  time,  it  follows 
that  speed  increases  with  accuracy.  The  increase  in  speed  with 
respect  to  accuracy  is  much  faster  than  the  increase  with  respect 
to  the  time  interval. 

Comparison  between  the  Speed  of  Recall  and  the  Amount 
of  Forgetting. 

The  increase  with  the  time  interval  in  the  number  of  seconds 
per  unit  recall,  as  further  complicated  by  the  degree  of  learning, 
may  be  compared  with  the  amount  of  forgetting  which  also  in¬ 
creases  with  time  and  varies  with  the  degree  of  learning.  The 
data  are  gathered  together  in  Table  XXV.  It  is  useless  to  com¬ 
pare  the  absolute  amount  of  forgetting  with  the  total  speed  of 
the  process,  since  only  in  the  light  of  the  general  shape  of  the 
curves  can  such  a  comparison  be  intelligible.  The  values  pre¬ 
sented  in  Table  XXV  are  converted  from  the  original  data,  using 
the  numerical  value  obtained  from  the  shortest  interval  in  each 
case  as  the  unit.  The  table  reveals  especially  the  relative  increase 
in  the  values  with  the  length  of  the  time  interval. 

In  spite  of  the  arbitrary  process  in  reducing  the  amount  of  for¬ 
getting  and  the  speed  of  recall  to  the  same  unitary  basis,  any 
graphical  representation  of  the  data  in  Table  XXV  would  still 
be  so  complicated  as  to  make  interpretation  impossible.  The 
curves  of  forgetting  may  be  said  to  be  logarithmic  in  a  sense, 
but  a  similar  mathematical  statement  would  no  longer  hold  for 
the  curves  for  the  speed  of  recall.  A  possible  generalization  one 
can  make  from  these  facts  is  that  the  curves  of  speed  do  not 
rise  as  rapidly  as  the  curves  of  forgetting.  The  decrease  in  the 
speed  of  recall  with  respect  to  the  length  of  the  time  interval  is  not 
as  rapid  as  the  decreases  in  the  total  amount  of  retention. 

So  the  amount  of  forgetting  and  the  speed  of  recall  do  not 
have  the  same  type  of  curves.  The  results  of  this  section  agree 
with  the  conclusion  reached  in  Ch.  II  concerning  the  difference 
between  the  relearning  and  the  other  methods,  only  we  have  at¬ 
tained  the  additional  observation  that  the  time  curves  differ 
among  themselves  even  more  radically  than  do  the  curves  of  for- 


72 


C.  W.  LUH 


TABLE  XXV 

Comparison  of  the  Amount  of  Forgetting  with  the  Speed  of 
Recall,  Taking  the  Numeeical  Value  of  the 


Shortest  Interval  as  Unit 

20  m. 

1  h. 

2  h. 

3  h. 

4  h. 

6  h. 

12  h. 

1  d. 

2  d. 

Writ.  Reprod. 

150%  learning 

Forgetting. . 

1. 00 

1.30 

1.51 

2.87 

3-8o 

5.12 

5-77 

Speed  . 

1. 00 

1.26 

1-37 

2.21 

2-53 

3-63 

4-53 

100%  learning 

Forgetting. . 

1. 00 

1-5 1 

3-74 

578 

6.36 

Speed  . 

1. 00 

1.24 

2.24 

3-53 

4.29 

67%  learning 

Forgetting. . 

1. 00 

1 .88 

2-34 

4.01 

5-15 

Speed  . 

1. 00 

1.94 

2.44 

3.50 

5.17 

33%  learning 

Forgetting. . 

1. 00 

1.42 

1.77 

2.28 

2.67 

Speed . 

1. 00 

1.78 

2.00 

3-39 

6.17 

Recognition 

150%  learning 

Forgetting. . 

1. 00 

.63 

•74 

1.70 

1.50 

4-53 

4-49 

Speed  . 

1. 00 

1. 18 

i-35 

1.56 

1.65 

1-43 

1.88 

100%  learning 

Forgetting. . 

1. 00 

.90 

2.35 

4.80 

5-23 

Speed . 

1. 00 

1.08 

1.28 

1.24 

1.40 

67%  learning 

Forgetting. . 

1. 00 

2.76 

4-59 

5-42 

8.52 

Speed  . 

1. 00 

1 .21 

1.44 

1-35 

1-57 

33%  learning 

Forgetting. . 

1. 00 

1.56 

2.13 

3-03 

3-28 

Speed . 

1. 00 

1. 18 

1. 14 

1.05 

1.29 

Reconstruction 

150%  learning 

Forgetting. . 

1. 00 

1.68 

2.68 

3-28 

3-00 

6.72 

10.88 

Speed  . 

1. 00 

1-37 

1-39 

1.70 

1-73 

2.08 

2.04 

100%  learning 

Forgetting. . 

1. 00 

1. 19 

2.00 

5-33 

5-02 

Speed . 

1. 00 

.82 

.91 

1. 16 

1. 18 

67%  learning 

Forgetting. . 

1. 00 

•99 

2.25 

3-87 

5-66 

Speed  . 

1. 00 

1.42 

1.29 

1-5  7 

i-57 

33%  learning 

Forgetting — 

1. 00 

1-33 

1.70 

2.03 

2.79 

Speed  . 

•  T*  « 

1. 00 

1.02 

1.30 

1. 10 

1. 18 

getting.  If  the  relearning  method  could  be  varied  and  controlled 


as  are  the  other  methods,  the  amount  of  “saving”  would  most 
probably  increase  or  decrease  according  to  various  conditions. 


VII.  INDIVIDUAL  DIFFERENCES  AND 

CORRELATIONS 


i.  Individual  Differences  in  Practice  Effect . 

It  has  been  sometimes  maintained  that  the  practice  effect  in 
learning  nonsense  material  disappears  after  the  successive  mas¬ 
tery  of  but  a  few  series.  In  our  experiments  we  had  the  oppor¬ 
tunity  to  plot  the  practice  curve  for  each  individual  subject. 
About  one-half  of  the  subjects  learned  more  than  50  series  each, 
thus  giving  rather  extensive  practice  curves.  From  the  com¬ 
parison  of  these  curves,  it  seems  that  the  extent  of  practice  effect 
is  subject  to  individual  differences.  For  most  of  the  subjects 
it  is  present  even  after  the  mastery  of  40  or  50  series,  and  it  de¬ 
creases  with  different  rates  for  different  individuals.  Three 
typical  curves  are  given  in  Fig.  XI  (Smoothed). 


Generally  speaking,  the  practice  effect  in  these  curves  seems  to 
have  disappeared  after  the  tenth  trial,  but  individual  differences 
are,  nevertheless,  present.  The  curve  for  subject  Y  has  an  abrupt 
initial  drop  which  is  not  so  prominent  in  the  other  curves.  That 
is,  he  adapted  himself  to  the  situation  more  quickly  than  did 
the  other  subjects.  The  readiness  with  which  one  adapts  to  this 
particular  situation  is  in  a  way  proportional  to  his  speed 
of  learning.  After  the  tenth  trial  the  gradual  fall  of  the  curves 
for  Le  and  Y  is  noticeable  to  the  very  end,  but  the  curve  for  Lo 
is  stationary.  So  individuals  differ  not  only  in  the  amount  of  the 
initial  drop,  but  also  in  the  gradual  decline  of  the  practice  effect. 
A  break  occurred  in  the  curve  for  Y  when  for  more  than  two 


73 


74 


C.  W.  LUH 


months  the  subject  did  not  work  on  nonsense  material.  The 
practice  effect  was  carried  over  that  interval. 

In  Ch.  Ill  it  was  mentioned  that  the  subjects  could  use  67% 
of  the  average  number  of  presentations  to  a  greater  advantage 
after  they  had  practiced  in  150%  and  100%  learning  for  more 
than  5  weeks.  This  improvement  in  learning  also  varied  greatly 
according  to  the  individual.  As  previously  stated,  we  took  an 
average  of  the  number  of  presentations  required  by  each  indi¬ 
vidual  for  the  mastery  of  the  20  syllable  series  in  100%  and 
150%  learning.  The  number  of  series  that  we  learned  with 
only  two-thirds  or  less  of  the  average  number  of  presentations, 
as  determined  for  each  individual,  was  exceedingly  small.  How¬ 
ever,  when  they  came  to  67%  learning,  most  of  the  subjects 
learned  one  or  more  of  the  series  with  that  number  of  presenta¬ 
tions.  Table  XXVI  shows  how  the  individuals  differ  in  this 
respect. 


TABLE  XXVI 


Series  Learned  with  2/3  or  Less  of  the  Average 
Number  of  Presentations 


I11  the  first  20-25  series 

subject 


B  1 

I  o 

Ka  2 

Ko  o 

Lud  2 

Luh  1 

S  2 

Wi  o 

Wo  1 


In  the  next  10 

3 

1 

3 
1 

1 

2 

4 

1 

2 
o 


2.  Individual  Differences  in  the  Speed  of  Learning. 

Table  XXVII  presents  the  average  number  of  presentations 
required  by  each  subject  to  learn  a  series  of  12  nonsense  syllables. 

It  takes  an  average  subject  about  14  presentations  to  learn 
a  series  of  12  nonsense  syllables  by  the  anticipation  method.  This 
average  is  just  a  little  higher  than  that  given  by  Finkenbinder.1 

The  two  groups  are  about  equal  in  efficiency,  for  as  already 


1  Op.  cit.,  pp.  21-22. 


THE  CONDITIONS  OF  RETENTION 


75 


TABLE  XXVII 

Average  Number  of  Presentations  for  Each  Series 


SUBJECT 

NO.  OF  PRESENTATIONS 

P.  E. 

NO.  OF  SERIES  LEARNED 

*Luh 

4.95 

.20 

20 

*Y 

6.42 

.18 

40 

Ko 

6.85 

.26 

20 

♦I 

8.75 

•33 

20 

*Wa 

9.42 

•27 

50 

*Le 

9.84 

.21 

50 

*c 

10.90 

•55 

20 

R 

11.88 

.32 

50 

DW 

13.26 

•37 

50 

Lo 

13-50 

.28 

50 

Lud 

13.65 

•33 

20 

Ka 

16.20 

•57 

20 

*S 

16.50 

.62 

20 

Wi 

17.20 

•37 

20 

*Ts 

18.10 

•54 

20 

B 

18.60 

•51 

20 

Kan 

1975 

.86 

20 

Wo 

19.80 

.65 

20 

*p 

24.50 

.67 

20 

Av. 

13.69 

^Chinese  students. 

indicated,  it  is  more  difficult  to  spell  a  syllable  letter  by  letter 
as  required  in  our  experiments  than  to  pronounce  it  as  a  whole 
as  required  by  Finkenbinder.  A  group  of  15  to  20  subjects  is, 
therefore,  large  enough  to  make  a  random  sample. 

The  fastest  learner  of  the  group  is  five  times  as  proficient  as 
the  slowest  learner.  On  the  whole,  the  Chinese  students  are  bet¬ 
ter  memorizers  than  the  Americans.  The  averages  stand  as  12.15 
against  15.07.  With  the  exception  of  subject  F,  the  difference 
would  be  much  higher.  Six  Chinese  occupy  the  first  seven  places. 
This  superiority  of  the  memorizing  ability  of  the  Chinese  is 
interesting  in  connection  with  the  problems  of  classical  training 
and  the  improvement  of  memory  with  practice. 

3.  Individual  Variability  in  the  Amount  of  Retention. 

100  S.  D. 

Applying  the  formula  V  = - ,  we  calculated  the 

Mean 

coefficient  of  variability  of  the  average  amount  of  retention  for 


76 


C.  W.  LUH 


the  five  methods  of  measurement  and  the  four  degrees  of  learn¬ 
ing.  These  coefficients  are  tabulated  in  Table  XXVIII. 

XXVIII 

Coefficients  of  Variability 


20  m. 

1  h. 

2  h. 

3  h. 

4  h. 

6  h. 

12  h. 

1  d. 

2  d. 

Anticipation. . . . 

26.2 

28.9 

41.0 

80.9 

133.3 

Relearning . 

18.1 

31.8 

22.6 

31.3 

34-3 

Writ.  Rcprod. 

150%  learning 

15.2 

17-5 

12.5 

26.9 

33-1 

77-1 

76.3 

100%  . 

6.8 

11 7 

27.0 

56.8 

70.4 

67%  . 

6.6 

28.5 

31.2 

48.1 

106.7 

33%  . 

17.8 

32.0 

38.5 

86.4 

115-5 

Recognition 

150%  learning 

34 

4-4 

6.6 

9.0 

15-2 

18.5 

18.9 

100%  . 

4-3 

5-8 

7-8 

22.9 

20.9 

67 % . 

11.3 

8.6 

13.2 

25.6 

31.8 

33%  . 

19.3 

1 6.6 

41.6 

62.9 

66. 5 

Reconstruction 

150%  learning 

15-6 

12.2 

9.8 

14.8 

23.8 

53-9 

69.8 

100%  . 

10.3 

1 2.7 

17.0 

46.3 

57-0 

67% . 

8.7 

21.3 

23.8 

28.7 

70.3 

33%  . 

22.4 

32.3 

41.4 

85.5 

78.4 

The  magnitude  of  the  coefficients  of  variability  for  the  long 
intervals  indicate  that  the  data  are  not  statistically  reliable. 
However,  our  present  problem  is  exactly  to  describe,  if  not  to 
interpret,  the  differences  in  statistical  reliability,  or  individual 
variability,  under  certain  conditions.  So  the  above  statement 
directly  leads  to  the  following  generalization. 

(i)  Individual  variability  increases  zvith  the  time  interval. 
This  factual  statement  holds  for  all  the  methods  of  measure¬ 
ment  and  all  degrees  of  learning.  The  tendency  can  be  more  dis¬ 
tinctly  observed  as  graphically  represented  in  Fig.  XII,  for  100% 
learning. 

These  graphs  are  based  on  similar,  and  in  some  cases  the  same 
numerical  values  as  are  the  retention  curves  in  Fig.  II.  A  com¬ 
parison  of  the  figures  brings  out  the  fact  that  the  curves  for  the 
coefficients  of  variability  have  not  only  preserved  the  particular 
order  of  the  different  methods  of  measurement,  a  proportionality 
of  the  absolute  differences  in  numerical  value,  but  to  some  extent, 
even  the  specific  similarity  or  dissimilarity  in  general  shape; 


THE  CONDITIONS  OF  RETENTION 


77 


they  also  manifest  that  characteristic  difference  between  relearn¬ 
ing  and  the  other  methods  of  measurement.  The  relearning 
curve  begins  as  the  second  in  height  in  the  order  of  variability 
but  ends  as  the  fourth,  having  crossed  the  written  reproduction 
and  reconstruction  curves  and  now  stands  half  way  between 
recognition  and  reconstruction  both  in  shape  and  numerical 
value.  The  significance  of  this  comparison  has  been  discussed 
at  length  in  Ch.  II,  where  it  was  pointed  out  that  relearning  is 
not  a  helpful  method  for  the  study  of  individual  differences. 

In  the  present  connection,  the  coefficients  of  variability  for 
the  different  intervals  as  determined  by  the  relearning  method 
fall  within  a  close  range  in  numerical  value.  Just  as  the  retention 
curve  for  relearning  is  complicated  by  involving  two  learning 
curves  for  memory,  so  also  the  corresponding  curve  for  the  co¬ 
efficients  of  variability  becomes  almost  unanalyzable  because  of 
the  same  complicaion.  In  Fig.  XII  the  asterisk  represents  the 


coefficient  of  variability  for  the  original  learning,  which  is  37.8. 
The  implications  of  the  “saving  method’’  would  lead  one  to 
expect  that  this  value  would  be  rather  close  to  the  average  value 
of  the  relearning  curve  in  the  same  figure. 

(2)  Individual  variability  increases  inversely  as  the  degree  of 


78 


C.  W.  LUH 


learning.  Exceptions  are  found  in  written  reproduction  and  re¬ 
construction  with  150%  learning  at  the  end  of  the  i-day  and 
2-day  intervals.  The  explanation  given  in  Ch.  V  for  the  char¬ 
acteristics  of  150%  learning  will  cover  the  present  instances. 

That  the  increase  in  the  degree  of  learning  should  tend  to 
equalize  and  finally  to  eliminate  individual  differences  is  also  to 
be  expected.  For  a  certain  degree  of  over-learning  will  make 
the  material  so  well  fixed  for  any  individual  who  can  fulfill  the 
requirements  of  these  experiments  that  the  amount  of  retention 
will  be  always  100%.  Such  are  our  habitual  and  conventional¬ 
ized  reactions  as  we  so  often  observe  in  daily  life.  The  varia¬ 
bility  of  these  reactions  approximates  o.  In  other  words,  the 
effect  of  increasing  the  degree  of  learning  upon  the  coefficient 
of  variability  approaches  o  as  a  limit. 

As  a  corollary  to  the  above  conclusion,  the  phenomenon  of 
diminished  returns  may  be  described  more  specifically.  Since 
the  increase  in  the  degree  of  learning  brings  about  diminished 
returns  in  the  amount  of  retention  and  at  the  same  time  neutral¬ 
izes  individual  variability,  it  follows  that,  in  the  long  run,  an 
individual  very  efficient  in  immediate  retention  is  not  likely  to 
improve  with  over-learning  as  rapidly  as  another  who  is  very  in¬ 
efficient  in  immediate  retention. 

(3)  Individual  variability  also  seems  to  be  a  function  of  the 
method  of  measurement  and  to  increase  with  the  number  of  re¬ 
stricting  factors  involved  in  the  recall  procesSj  as  explained  in 
Ch.  II. 

*  / 

(4)  Summarizing  (1),  (2)  and  (3),  individual  variability  in 
retention  increases  with  the  difficidty  of  the  act  and  decreases 
with  the  frequency  and  the  recency  of  practice. 

4.  Correlation  between  the  Speed  of  Learning  and  the  Amount 
of  Retention. 

The  formula  used  is 

62D2  7T 

P  =  1 - .  Then  r  =  2  sin  ( — p) 

N(N2  —  1)  v6 

1  —  r2 

and  P.  E.  =  .703  - .  Table  XXIX  gives  the  correlations 

VN 


THE  CONDITIONS  OF  RETENTION 


79 


whose  numerical  values  are  at  least  twice  as  large  as  their  re¬ 
spective  P.  E/s. 

TABLE  XXIX 

Correlation  between  the  Speed  of  Learning  and  the 
Amount  of  Retention 


Relearning . 

P.  E . 

Anticipation 

P.  E . 

Writ.  Reprod. 

150%  learning 

P.  E . 

100%  . 

P.  E . 

67%  . 

P.  E . 

33%  . 

'  P.  E . 

Recognition 

150%  learning 

P.  E . 

100%  learning 

P.  E . 

67%  learning 

P.  E . 

33%  . 

P.  E . 

Reconstruction 

•  150%  learning 

P.  E . 

100%  learning 

P.  E . 

67%  learning 

P.  E . 

33%  learning 

P.  E . 


20  m.  1  h.  2  h. 
—.42 
.18 


•30  40 

.15  .14 

.40 

19 


•59 

.14 

•39  -32 

.14  .15 

.42 
.18 


•50 

•  1 7 


•58 
•  15 
.41 
•19 


3  h.  4I1.  6h.  12  h.  id.  2d. 

—.42 

.18 

•51 

.18 


•43 

.18 


•50 
•i  7 


•53  —.47 

.16  .17 

•37 

.14 


— .64 
•13 


—.40  —.57 
.19  .15 


•44 

.18 


The  correlation  values  are  all  positive  except  two  in  relearning, 
four  in  recognition  and  one  in  reconstruction,  and  the  chances  are 
at  least  4.5  to  1  that  the  data  will  be  reproduced  in  another  series 
of  experiments  with  as  few  as  ten  subjects. 

The  negative  correlation  between  learning  ability  and  the 
amount  of  retention  as  measured  by  the  “saving  method”  is  an 
obvious  consequence  of  the  method  of  computation.  Let  X  and 


8o 


C.  W.  LUH 


Y  represent  the  number  of  presentations  involved  in  learning  and 

c 

relearning  respectively.  Then  X  and  —  will  represent  deficiency 

X 


and  proficiency  of  learning  ability  respectively,  and 


X  — Y 

IT 


or 


Y 


i - will  represent  the  percentage  value  of  retention  as 

X 

Y 

measured  by  the  "saving  method,"  in  which  the  fraction  —  will 

X 

c 

have  a  value  less  than  i.  The  negative  correlation  between  —  and 


X 


Y 

X 


which  we  secured  means  a  positive  correlation  between 

Y 

X  and  i - -  and  this  is  necessarily  due  to  a  negative  correlation 

X 

r  r  Y  .  Y 

between  X  and  — ,  for  as  X  increases,  the  value  of  i - can 

X  X 


increase  only  as  the  value  of  the  fraction  —  decreases. 

X 

Y 

This  negative  correlation  between  X  and  -  will  naturally 

X 

occur  because  of  the  presence  of  X  in  both  values  whenever  the 
following  relations  between  X  and  Y  obtain: 

1.  Absence  of  correlation. 

2.  A  negative  correlation. 

increment  Y 

3.  A  positive  correlation  when  - — ; -  is  less  than 


Y 


increment  X 
~X~~ 


c  Y 

In  other  words,  the  correlation  between  —  and  1 - is  neces- 

X  X 

sarily  negative  unless  X  and  Y  are  positively  correlated  and  at 


THE  CONDITIONS  OF  RETENTION 


81 


increment  Y 

the  same  time  fulfill  the  condition  that - is  equal  to 

Y 

increment  X 
or  greater  than - . 

X 

The  actual  correlation  between  X  and  Y  determined  in  these 
experiments  is  positive,  as  presented  in  Table  XXX.  The  re¬ 
quired  relation  between  the  increments  of  X  and  Y  cannot  be 
determined  very  easily.  However,  considering  the  phenomenon 
of  diminished  returns  in  the  learning  curve,  such  a  relation  be¬ 
tween  X  and  Y  is  very  unlikely.  There  is  more  material  to  be 
mastered  in  the  original  learning  than  in  relearning.  Hence,  the 
increments  of  X  due  to  deficiency  in  learning  ability  will  as  a 
rule  be  proportionally  as  well  as  absolutely  greater  than  the  re¬ 
spective  increments  of  Y. 

Thus,  the  negative  correlation  which  we  ascertained  between 
learning  ability  and  the  amount  of  “saving”  is  a  consequence  of 
the  fact  that  X  is  involved  in  both  values.  It  is  merely  a  product 

i 

of  a  negative  correlation  between  X  and  — ,  and  a  positive  cor- 

X 

relation  between  X  and  Y  which  we  secured.  A  negative  cor¬ 
relation  will  also  obtain  under  almost  every  possible  relation  be¬ 
tween  X  and  Y.  The  correlation  thus  has  no  significance  as  to 
learning  ability  and  retention. 

This  analysis  confirms  our  previous  contentions  that  the  re¬ 
learning  method  constitutes  a  poor  measure  of  retention. 


TABLE  XXX 

Correlation  between  the  Speed  of  Learning 
and  of  Relearning 


20  m. 

1  h. 

4  h. 

1  d. 

2  d. 

Correlation  . 

. 50 

.21 

.98 

•35 

•78 

P.  E . 

. 1 7 

.21 

.01 

.20 

.09 

With  the  exception  of  relearning,  the  remaining  data  may  be 
easily  summarized  as  follows: 

(i)  With  the  recognition  method  and  possibly  also  recon¬ 
struction,  the  correlation  between  the  speed  of  learning  and  the 
amount  of  retention  tends  to  change  from  positive  to  negative 


82 


C.  W.  LUH 


as  the  interval  is  lengthened.  The  fast  learners  tend  to  be  the 
least  efficient  in  recognition  for  the  comparatively  longer  inter¬ 
vals, 

(2)  With  the  written  reproduction  method,  the  correlation 
between  the  same  factors  is  always  +,  if  there  is  any  correlation 
at  all.  The  fastest  learners  are  as  a  rule  the  best  retainers. 

(1)  and  (2)  together  might  suggest  that  the  two  memory 
processes  differ  in  quality  as  well  as  in  quantity,  but  our  data  are 
not  conclusive. 

(3)  While  the  increase  in  the  degree  of  learning  tends  to 
equalize  individual  differences,  it  does  not  at  the  outset  min¬ 
imize  the  numerical  value  of  certain  correlations.  On  the  con¬ 
trary,  up  to  150%  learning,  increase  in  learning  seems  to  make 
the  correlation  between  learning  and  retention  more  definite  and 
reliable. 

It  seems  to  the  present  writer  that  a  more  careful  study  of  the 
correlation  between  the  above  two  factors  is  the  only  systematic 
way  to  approach  the  difference  between  “immediate’’  and  “per¬ 
manent”  memory.  Sometimes  it  has  been  asserted  that  recall 
immediately  after  learning  differs  from  delayed  recall  in  nature 
.  as  well  as  in  quantity.2  One  forgets  that  immediate  recall  is 
recall  after  a  neglected  interval.  It  is  neglected  because  it  is  too 
short  to  be  appreciable.  The  control  of  this  interval  will  deter¬ 
mine  a  point  on  the  curve  of  retention  just  as  any  other  point. 
Besides  certain  questionable  introspective  conclusions,  the  chief 
reason  for  differentiating  “immediate”  and  “permanent”  reten¬ 
tion  in  that  way  is  the  negative  correlation  that  has  occasionally 
been  discovered  between  the  speed  of  learning  and  the  amount  of 
retention.  The  relearning  method  was  often  used  for  this  pur¬ 
pose  and,  for  some  unknown  reason  or  another,  one  particular 
time  interval  was  chosen.  Now  we  have  discovered  that  the 
numerical  value  of  the  correlation  for  the  same  group  of  sub¬ 
jects  changes  under  various  conditions.  It  varies  with  the  method 
of  measurement,  the  degree  of  learning,  the  length  of  the  time 
interval,  and  perhaps  with  every  variable  condition  that  we  can 
mention.  Similar  variations  will  most  probably  be  found  in  the 
correlation  values  for  “permanent”  memory  measured  for  two 
2  E.  g.,  E.  Meumann,  “The  Psychology  of  Learning,,  Eng.  Tr.,  pp.  40  ff. 


THE  CONDITIONS  OF  RETENTION 


83 


different  intervals.  The  objective  reason  for  differentiating  “im¬ 
mediate”  and  “permanent”  memory  is,  therefore,  unsound. 

5.  Correlation  between  the  Speed  of  Learning  and  the  Speed 
of  Recall. 

The  data  are  presented  in  Table  XXXI.  Like  Table  XXX,  it 
contains  only  the  correlation  values  which  are  at  least  twice  as 
high  as  their  respective  P.  E.’s. 


TABLE  XXXI 

Correlation  between  the  Speed  of  Learning  and  the 

Speed  of  Recall 


20  m. 

1  h. 

2  h. 

3  h. 

4  h. 

6h.  12  h. 

1  d. 

2  d. 

Writ.  Reprod. 

150%  learning 

.42 

P.  E . 

.18 

loo  % . 

•55 

.61 

P.  E . 

.11 

.10 

67% . 

.70 

.61 

.40 

P.E . 

.11 

.14 

.19 

33%  . 

•51 

•43 

.69 

49 

P.  E . 

.16 

.18 

.12 

47 

Recognition 

150%  learning 

.60 

.42 

—45 

—47 

P.  E . 

.14 

.18 

.18 

•1 7 

100%  . 

.58 

.56 

P.  E . 

.11 

.11 

67%  . 

—•63 

P.  E . 

43 

33%  . 

P.  E . 

Reconstruction 

150%  learning 

•71 

.48 

.72 

.41 

P.  E . 

.11 

.17 

.11 

.19 

100%  . 

•36 

•34 

P.  E . 

.14 

.14 

67%  . 

.48 

—•73 

P.  E . 

.17 

.10 

33%  • 
P.  E 


The  speed  of  recall  for  written  reproduction  is  taken  to  be  the 
number  of  seconds  per  unit  material.  For  recognition  and  recon¬ 
struction,  it  is  the  total  duration  of  the  recall  process  in  number 
of  seconds. 

Negative  values  are  again  found  in  recognition  for  the  longer 
intervals.  The  slow  learners  are  not  only  more  proficient  in  recog¬ 
nition  memory  in  the  long  run,  but  they  also  recognize  the  ma- 


84 


C.  W.  LUH 


terial  much  faster.  Another  solitary  negative  value  appears  in 
reconstruction.  Its  significance  is  probably  the  same  as  for  the 
negative  recognition  values.  Otherwise,  the  faster  learner  also 
tends  to  be  the  faster  in  recall.  This  correlation  is  most  prob¬ 
ably  due  to  the  fact  that  the  faster  learners  are  also  more  pro¬ 
ficient  retainers.  So  we  present  in  the  next  section  the  correla¬ 
tion  between  the  amount  and  the  speed  of  recall. 

6.  Correlation  between  the  Amount  and  the  Speed  of  Recall . 

TABLE  XXXII 

Correlation  between  the  Amount  and  the  Speed  of  Recall 


20  m. 

1  h. 

2  h. 

3  h. 

4  h. 

6  h. 

12  h. 

1  d. 

2  d 

Writ.  Re  prod. 

150%  learning 

.84 

.80 

•72 

.96 

.78 

.96 

.61 

P.  E . 

.06 

.08 

.11 

.02 

.09 

.02 

.14 

100%  . 

.60 

.71 

•73 

.76 

•50 

P.  E . 

.10 

.08 

.07 

.06 

.12 

67%  . 

.65 

.89 

•97 

.62 

.60 

P.  E . 

•13 

.05 

.01 

.14 

.14 

35%  . 

•65 

.82 

.80 

.89 

P.  E . 

•13 

.07 

.08 

•05 

Recognition 

150%  learning 

•77 

.60 

.81 

•50 

•44 

P.  E . 

.09 

.14 

.08 

•17 

.18 

100%  . 

•63 

•47 

•59 

•34 

.62 

P.  E . 

.10 

•  13 

.11 

.14 

.10 

67%  . 

.62 

.76 

.64 

•43 

P.  E . 

.14 

.09 

•13 

.18 

33%  . 

.38 

•43 

P.  E . 

.19 

.18 

Reconstruction 

150%  learning 

•73 

•45 

.61 

.42 

P.  E . 

.10 

.17 

.14 

.18 

100%  . 

.72 

•71 

.42 

•54 

P.  E . 

.08 

.08 

•13 

.12 

67%  . 

—47 

P.  E . 

•17 

33%  . 

•53 

•45 

P.  E . 

.16 

.17 

The  individual  who  retains  the  most  also  tends  to  recall  it  the 
most  readily.  With  the  exception  of  a  single  negative  value  in 
reconstruction,  this  tendency  is  independent  of  the  speed  of 
learning  and  does  not  seem  to  vary  according  to  the  method  of 
measurement,  the  degree  of  learning  or  the  length  of  the  time 
interval. 


VIII.  CONCLUSION 

i.  The  curve  of  retention  varies  with  the  method  of  measure¬ 
ment. 

A)  The  curve  as  determined  by  the  “saving  method”  differs 
both  in  height  and  general  shape  from  all  the  other  curves  deter¬ 
mined  by  methods  which  directly  measure  the  amount  of  reten¬ 
tion.  For  the  comparatively  shorter  intervals,  the  relearning 
curve  falls  more  rapidly  than  does  most  any  curve,  but  the  ten¬ 
dency  is  reversed  for  the  longer  intervals.  This  difference  in 
the  shape  of  the  curves  follows  as  a  mathematical  necessity  from 
the  predetermined  differences  in  the  units  of  measurement. 

B)  Aside  from  the  relearning  curve,  the  other  curves  stand  in 
the  order  o±  their  numerical  values  as  follows :  Recognition  is 
the  first,  reconstruction  the  second,  written  reproduction  the 
third  and  anticipation  the  last.  Many  reasons  may  be  given  for 
these  particular  numerical  differences,  but  above  all  the  order  of 
the  curves  is  a  function  of  the  number  of  restricting  factors  in¬ 
volved  in  the  conditions  of  recall. 

C)  In  spite  of  the  variations  in  the  methods  of  measurement, 
the  curves  are,  on  the  whole,  more  similar  to  that  of  Ebbinghaus 
than  to  those  of  Ballard. 

D)  In  numerical  value,  our  retention  curve  for  relearning 
approaches  most  closely  to  that  of  Finkenbinder,  but  our  recog¬ 
nition  curve  is  vastly  different  from  that  of  Strong.  The  simi¬ 
larity  of  data  depends  upon  the  corresponding  similarity  of  tech¬ 
nique. 

2.  The  curve  of  retention  varies  with  the  degree  of  the  original 
learning.  The  amount  of  retention  for  most  intervals  increases 
with  the  degree  of  learning. 

A)  Increase  in  the  degree  of  learning  favors  the  more  diffi¬ 
cult  methods  for  the  longer  intervals. 

B)  The  effect  of  the  increase  in  the  degree  of  learning  upon 
the  amount  of  retention  manifests  the  phenomenon  of  diminished 

85 


86 


C.  W.  LUH 


returns.  This  phenomenon  is  the  incidental  and  almost  necessary 
consequence  of  the  tendency  of  negative  acceleration  obviously 
present  in  the  learning  curve  for  memory. 

C)  On  the  whole,  the  curves  of  retention  for  the  different 
degrees  of  learning  still  approach  more  closely  to  the  Ebbinghaus 
type  than  to  that  of  Ballard.  The  recognition  curves  are,  how¬ 
ever,  far  from  being  logarithmic. 

3.  Beyond  a  certain  limit,  the  duration  of  the  recall  process 
has  but  little  effect  upon  the  amount  of  recall  or  the  curve  of 
retention. 

A)  The  shape  of  the  retention  curve  for  written  reproduction 
is  practically  determined  at  the  end  of  the  first  2  min.  of  recall. 
For  recognition  90  sec.  of  recall  is  long  enough  for  determining 
the  shape  of  the  curve. 

B)  With  the  written  reproduction  method,  the  effect  of  ex¬ 
tending  the  time  limit  for  recall  upon  the  amount  of  reproduction 
is  negatively  accelerative. 

4.  The  amount  of  error  in  written  reproduction  increases  with 
the  time  interval,  but  the  error  curve  thus  determined  manifests 
no  definite  relationship  to  the  curve  of  forgetting  which  also 
rises  with  the  time  interval.  Nevertheless,  the  former  has  to  be 
taken  account  of  as  a  supplementary  curve  of  retention. 

5.  The  speed  of  recall  decreases  with  the  time  interval,  but  the 
speed  curve,  too,  bears  no  similarity  or  causal  relation  to  the 
curve  of  forgetting,  though  it  is  indicative  of  the  conditions  of 
retention. 

6.  A)  Individual  variability  increases  with  the  difficulty  of 
the  act  of  recall,  but  decreases  with  the  frequency  and  the  recency 
of  practice. 

B)  The  speed  of  learning  and  the  amount  of  retention  are 
positively  correlated. 

The  results  of  these  experiments  prove  that  the  difference 
between  the  Ebbinghaus  tradition  and  the  type  of  curve  discov¬ 
ered  by  Ballard  is  not  due  to  differences  (1)  in  the  method  of 
measurement  or  (2)  in  the  degree  of  the  original  learning. 

We  do  not  find  a  higher  amount  of  retention  for  the  2-day 


THE  CONDITIONS  OF  RETENTION 


8  7 


interval  than  for  i  day  or  even  immediate  recall,  as  did  Ballard. 

Differing  from  the  Ebbinghaus  tradition,  our  curves  are  not 
all  logarithmic.  Some  of  the  recognition  curves  do  not  even 
manifest  the  phenomenon  of  negative  acceleration  in  general. 

The  curve  of  retention  varies  with  the  conditions  of  learning 
and  of  recall. 


I 


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